In the annual battle of the dorms, students gather on the roofs of Jackson and Walton dorms to launch water balloons at each other with slingshots. The horizontal distance between the buildings is 35.5 m, and the heights of the Jackson and Walton buildings are, respectively, 15.5 m and 22.5 m. Ignore air resistance.
(a) The first balloon launched by the Jackson team hits Walton dorm 2.2 s after launch, striking it halfway between the ground floor and the roof. Find the direction of the balloon's initial velocity. Give your answer as an angle measured above the horizontal.
(b) A second balloon launched at the same angle hits the edge of Walton's roof. Find the initial speed of this second balloon.
Answers
The basic kinematic equations for horizontal and vertical motion are as follows:
s = v₀t + ¹/₂at²
Horizontal motion is:
x = v₀ₓt + ¹/₂aₓt²
x = v₀ₓt
x = v₀ cosαt
Because there is no air resistance: x = v₀ cosθt
Vertical motion is:
y = v₀[tex]__y[/tex]t + ¹/₂a[tex]__y[/tex]t²
y = v₀ sinαt - ¹/₂gt²
Solve both for the velocity trigonometric function term as follows:
y = v₀ sinαt - ¹/₂gt²
v₀sinαt = ¹/₂gt² + y
v₀sinα = ¹/₂gt² + y/t
and
x = v₀ cosαt
v₀cosα = x/t
Now divide these two equations and we get
v₀sinα/v₀cosα = tanα [tex]=\frac{1/2gt + \frac{y}{t} }{\frac{x}{t} }[/tex]
tan α [tex]= \frac{1/2gt + \frac{y}{t} }{\frac{x}{t} } = \frac{gt^2}{2x} + \frac{y}{x}[/tex]
tan α [tex]= \frac{gt^2}{2x} + \frac{y}{x}[/tex]
Enter a value, x is the distance between the boarding 35.5 m, and y is the difference between the launch height and the drop point. The launch height is 15.5 m and the landing height is 11.0 m, so y = -4.5 m. Finally, we are told the projectile travel time is 2.2 s.
tan α [tex]= \frac{gt^2}{2x} + \frac{y}{x}[/tex]
tan α [tex]= \frac{(9.8)(2.2)^2}{2(35.5)} + \frac{-4.5}{35.5}[/tex]
tan α [tex]= 0.668 - 0.126[/tex]
tan α [tex]= 0.542[/tex]
α = tan⁻¹ 0.542
α = 28.4°
For the second launch, y₂ is +7.0 m launch altitude is still 15.5 m, but the deployment altitude is now 22.5 m, and x is still 35.5 m. The angle remains 28.4°. This time we don't know the flight time or initial velocity we are asked to find. Using horizontal distances, we can solve for time.
x = v₀.cosα.t
t² = x/v₀.cosα
Now do it for y₂:
y₂ [tex]= v_0sin(\alpha) t - 1/2gt^2[/tex]
y₂ [tex]= v_0sin(\alpha) (\frac{x}{v_0cos(\alpha)} ) - 1/2g (\frac{x}{v_0cos(\alpha)} )^2[/tex]
y₂ [tex]= x tan (\alpha ) - \frac{gx^2}{2v_0cos(\alpha)^2}[/tex]
[tex]\frac{gx^2}{2v_0cos(\alpha)^2} = x tan (\alpha ) - y_2[/tex]
We need to solve v₀:
[tex]\frac{gx^2}{2v_0cos(\alpha)^2} =\frac{1}{ x tan (\alpha ) - y_2}[/tex]
2v₀cos (α)² [tex]= \frac{gx}{ x tan (\alpha ) - y_2}[/tex]
v₀² [tex]= (\frac{1}{2cos(\alpha)^2} ) \frac{gx}{ x tan (\alpha ) - y_2}[/tex]
v₀² [tex]= (\frac{x^2}{cos(\alpha)^2} ) \frac{g/2}{ x tan (\alpha ) - y_2}[/tex]
v₀² [tex]= (\frac{x}{cos(\alpha)^2} ) \sqrt{ \frac{g/2}{ x tan (\alpha ) - y_2}}[/tex]
Now we can enter values:
v₀² [tex]= (\frac{x}{cos(\alpha)^2} ) \sqrt{ \frac{g/2}{ x tan (\alpha ) - y_2}}[/tex]
v₀² [tex]= (\frac{35.5}{cos(28.4^0)} ) \sqrt{ \frac{9.8/2}{ 35.5 tan (28.4^0) - 7.0}}[/tex]
v₀² = 40.386 [tex]\sqrt{\frac{4.9}{12.17} }[/tex]
v₀² = 40.386 (0.634)
v₀² = 25.62 m/s
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Related Questions
Two protons (charge q = 1.602·10-19 C) move at the same speed v= 1.6 ·105 m/s in opposite directions parallel to the x-axis. At the instant when they are at the same x-position, the proton moving in the negative direction is at distance r= 0.7 m in the positive y-direction with respect to the one moving in the positive direction. What is the magnetic field direction at the point of the proton moving in the negative direction? What is the magnetic force direction experienced by the proton moving in the negative direction?
Answers
The magnitude of the magnetic field at the point of the proton moving in the negative direction is equal to 18.39 × 10⁻¹⁵ T.
The magnetic force direction that is experienced by the proton moving in the negative direction is equal to 4.71 x 10⁻²⁸ N.
What is the magnetic field due to proton?The magnitude of the magnetic field at distance 'r' at the point of the proton moving in the negative direction is determined as follows;
F = qvB = (kq²)/r²
qvB = kq²/r²
B = kq/vr²
where, k is the coulomb's constant, r is the distance between the protons, q is the magnitude of the charge of the protons, and v is the speed of the proton.
Given the charge n the proton, q = 1.602 x 10⁻¹⁹C
The speed of the proton, v = 1.6 x 10⁵ m/s
B = (9 x 10⁹ x 1.602 x 10⁻¹⁹) / (1.6 x 10⁵ m/s x 0.7 x 0.7)
B = 18.39 × 10⁻¹⁵ T
The magnetic force experienced by the proton in the negative direction is calculated as follows;
F = qvB
F = 1.602 x 10⁻¹⁹ x 1.6 x 10⁵ x 18.39 × 10⁻¹⁵ T
F = 47.1 x 10⁻²⁹ N
F = 4.71 x 10⁻²⁸ N
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The terminals of a battery are connected across two resistors in parallel. The resistances of the resistors are not the same. Which of the following statements is correct? Choose all that are correct. The potential difference is greater across the resistor closer to the battery. The resistor with the larger resistance carries less current than the other resistor. The resistor with the larger resistance carries more current than the other resistor. The potential difference across the larger resistor is greater than the potential difference across the smaller resistor. The potential difference across each resistor is the same.
Answers
Answer:
1) the potential difference is the same for both resistors
2) the larger resistor must carry less current because of (1)
3) the potential difference is the same for both resistors - given (everything depends on this fact)
The work done in pushing a 40 kg chair from the kitchen table to 10 meters down the
hall would be about “blank”
neglecting friction.
Answers
The work done in pushing a 40 kg chair from the kitchen table to 10 meters down the hall would be 3920 Nm.
What is gravitational force?Gravity, also called gravitational force in mechanics, is the universal force of attraction that acts between all matter. It is the weakest of the known forces in nature, and therefore plays no role in determining the internal properties of everyday matter. It controls the orbits of objects, stars, galaxies, and the universe as a whole, as well as the structure and evolution of objects elsewhere in the universe.
On Earth, every object has a weight, or downward gravitational force, proportional to its mass. , the mass of the Earth acts on them. Gravity is measured by the acceleration it imparts to a free-falling object. At the Earth's surface, the acceleration of gravity is approximately 9.8 meters (32 feet) per second. For each second her body is in free fall, its velocity increases by about 9.8 meters per second. On the moon, the acceleration of a free-falling object is approximately 1.6 meters per second.
Gravitational force on chair:
F = mg
When, F = force
m = mass of chair (40 kg)
g = gravitational acceleration (9.8 m/s²)
F = 40 × 9.8
F = 392 N
For work done:
W = F × s
Where, w = work done
F = force (392 N)
s = distance (10 m)
W = 392 × 10
W = 3920 Nm
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Three electromagnetic waves travel through a certain point P along an x axis. They are polarized parallel to a y axis, with the following variations in their amplitudes. Find their resultant at P
E1 =(10.0μV/m)sin[(2.0×10^14rad/s)t]
E2 =(5.00μV/m)sin[(2.0×10^14rad/s)t+45.0∘]
E3 =(5.00μV/m)sin[(2.0×10^14rad/s)t−45.0∘]
Answers
Their resultant at point P is 17.07μV/m.
What is electromagnetic waves?Electromagnetic waves are a type of energy wave that has both electric and magnetic field components. They are created by the movement of electrically charged particles and travel through space at the speed of light. Electromagnetic waves can be used for communication, radiation, and other purposes. They are also responsible for the electromagnetic spectrum, which ranges from high-energy gamma rays to low-energy radio waves. Electromagnetic waves are used in a variety of applications, such as radio and television broadcasts, cellular phone communications, and radar. They can also be used to diagnose medical conditions and to detect objects in space. Electromagnetic waves are used in scientific research and are important in the understanding of the universe.
The amplitude of first wave,a1 = 10.0μV/m
The amplitude of second wave, a2 = 5.00μV/m
The amplitude of third wave, a3 = 5.00μV/m
Phase angle of first wave, θ1 = 0°
Phase angle of second wave, θ2 = 45°
Phase angle of third wave , θ3 = -45°
Their resultant at point P is given by ,
R = a1 Cosθ1 + a2 Cos θ2 + a3 Cosθ3
= 10 * Cos0 + 5 * Cos(45) + 5 * Cos(-45)
=17.07μV/m
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A neutron in a reactor makes an elastic head-on collision with the nucleus of an atom initially at rest.
Assume: The mass of the atomic nucleus is
about 12.4 the mass of the neutron.
What fraction of the neutron’s kinetic energy is transferred to the atomic nucleus?
If the initial kinetic energy of the neutron is
5.53 × 10−13 J, find its final kinetic energy.
Answer in units of J.
Answers
(a) The fraction of neutron's kinetic energy transferred to the atomic nucleus is 0.08.
(b) The final kinetic energy of the neutron is 5.08 x 10⁻¹³ J.
What is the final velocity of the atom?The final velocity of the atom is calculated by applying the principle of conservation of linear momentum as follows;
initial momentum of the neutron = final momentum of the atomic nucleus
m₁u₁ = m₂u₂
where;
m₁ is the mass of the neutronu₁ is the initial velocity of the neutronm₂ is the mass of the atomic nucleus u₂ is the final velocity of the atomic nucleusThe mass of the atomic nucleus = 12.4 m₁
u₂ = m₁u₁ / m₂
u₂ = m₁u₁ / (12.4 m₁)
u₂ = 0.08u₁
The initial kinetic energy of the neutron is calculated as;
K.Ei = ¹/₂m₁u₁²
The final kinetic energy of the atomic nucleus is calculated as;
K.Ef = ¹/₂m₂u₂²
K.Ef = ¹/₂(12.4 m₁)(0.08u₁)²
K.Ef = 0.08 (¹/₂m₁u₁²)
K.Ef = 0.08 (K.Ei)
The fraction of neutron's kinetic energy transferred to the atomic nucleus is calculated as;
= 0.08 (K.Ei) / K.Ei
= 0.08
= 8 %
The final kinetic energy of the neutron is calculated as follows;
K.E.f (neutron) = (1 - 0.08) x (5.53 x 10⁻¹³ J)
K.E.f (neutron) = 5.08 x 10⁻¹³ J
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_NO+_O2 > _NO2 balance this
Answers
Answer:
4NO+2O2------>4NO2
that's the answer
A baseball player uses a pitching machine to help him improve his batting average. He places the 73.9 kg machine on a frozen pond. The machine fires a 0.118 kg baseball horizon-
tally at a speed of 40.8 m/s. What is the magnitude of the recoil velocity
of the machine?
Answer in units of m/s.
Answers
According to the law of conservation of momentum, the magnitude of the recoil velocity of the machine is equal to the magnitude of the initial velocity of the baseball, since the total momentum of the system (the machine and the baseball) remains constant. In this case, the magnitude of the initial velocity of the baseball is 40.8 m/s, so the magnitude of the recoil velocity of the machine is also 40.8 m/s. Answer: \boxed{40.8}.
BRAINLIEST -- 11 pts
A 2,713 kg van runs into the back of a 843 kg compact car at rest. They move off together at 6.9 m/s. Assuming the friction with the road is negligible, calculate the initial speed of the van.
WILL GIVE BRAINLIEST!!!!
explanation is preferred so i can learn but not necessary
Answers
Answer: approximately 9.02 m/s.
Explanation: In this scenario, we can use the conservation of momentum to determine the initial speed of the van. Momentum is defined as the product of an object's mass and velocity, and it is conserved in collisions where there is no net external force. This means that the total momentum of the van and car before the collision must be equal to the total momentum of the van and car after the collision.
We can write this as an equation:
2,713 kg * v1 + 0 kg * 0 m/s = 2,713 kg * 6.9 m/s + 843 kg * 6.9 m/s
where v1 is the initial speed of the van. Solving for v1, we get:
v1 = (2,713 kg * 6.9 m/s + 843 kg * 6.9 m/s) / 2,713 kg
= 6.9 m/s + (843 kg * 6.9 m/s) / 2,713 kg
= 6.9 m/s + 3.12 m/s
Therefore, the initial speed of the van was approximately 9.02 m/s.
The mass of earth is 5.97 x 10²⁴kg, the mass of the moon is 7.35 x 10²² kg and the mean distance of the moon from the center of Earth is 3.84 X 10⁵ km. Calculate the magnitude of the gravitational force exerted by earth on the Moon
Answers
The magnitude of the gravitational force exerted by earth on the moon will be equal to 1.85 × 10⁵ N.
What is gravity?The fundamental force of attraction operating on all matter is recognized as gravity, also spelled gravity, in mechanics. It has no impact on identifying the interior properties of common matter because it is the weakest force known to exist in nature.
The formation and growth of planets, galaxies, and the universe are all under the influence of this long-range, cosmic force, which further determines the trajectories of objects throughout the universe and the entire universe.
As per the given information in the question,
Mass of earth, M₁ = 5.97 × 10²⁴ kg
Mass of moon, M₂ = 7.35 x 10²² kg
Distance between moon from center of earth, r = 3.84 X 10⁵ km
G = 6.67×10¹¹ Nm² / kg²
Use the formula of force,
F = GM1M2 / r²
F = [(6.67×10¹¹) (5.97 × 10²⁴)(7.35 x 10²²)]/( 3.84 X 10⁵)²
F = 1.85 × 10⁵ N
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if beam (1) is the incoming beam in the figure, which of the other four red lines are reflected beams and which are refracted beams? (select all that apply.) reflected beams 2 3 4 5 refracted beams 2 3 4 5
Answers
Beams that bounce off a surface and continue to travel through that same medium are said to be reflected. However, because of this The refracted beams are 3, 5, and the reflected beams are 2, 4, and 2.
What other term do you use to describe reflecting?Cogitate, deliberate, reason, conjecture, and think are some typical synonyms of reflect. While each of these phrases means "to utilize one's skills of imagination, judgment, or inference," "reflect" denotes thoughtful deliberation about a memory.
Use reflect in what ways?To contemplate something thoroughly and deeply I must think for a while before making a choice. Think about or consider something She was given some alone time to consider the effects of her choice. show that... The interview had gone well, he thought as he was driving home.
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If a football quarterback runs into and tackles another player by grabbing onto them, what type of collision would this technically be?
a. Elastic
b. Inelastic
Which of the following would be an example of a closed system?
a. A person pushing a refrigerator box across a rough floor
b. A water bucket being pulled up by rope from a well
c. A rolling oil drum across a smooth, frictionless marble floor
d. A large moving rock slowing down while ploughing through loose sand
Answers
''If a football quarterback runs into and tackles another player by grabbing onto them'' is Elastic collision. A closed system is a rolling oil drum across a smooth, frictionless marble floor.
What is meant by Elastic collision?A collision between two bodies in physics is referred to as an elastic collision if their combined kinetic energy stays constant. There is no net conversion of kinetic energy into other forms, such as heat, noise, or potential energy, in an ideal, fully elastic collision.When two small objects collide, the kinetic energy of the collision is first transformed into the potential energy of an attractive or repulsive force between the particles. (when the particles move against this force, that is, when the angle between the force and the relative velocity is acute), and then this potential energy is transformed back into the kinetic energy of the collision (when the particles move with this force, i.e. the angle between the force and the relative velocity is acute).Learn more about Elastic collision refer to :
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For total internal reflection to occur, all of the following must happen but __________. Question 4 options: light must travel slower in the first medium light must refract light must strike the boundary at an angle greater than the critical angle the boundary must be reflective
Answers
For total internal reflection to occur, all of the following must happen but light must travel slower in the first medium.
What is the total internal reflection?Total internal reflection, can be described as the complete reflection of a ray of light within a medium however this medium could be water or glass from the surrounding surfaces back into the medium.
It should be noted that the total internal reflection will not take place unless the incident light is traveling within the more optically dense medium , hence phenomenon occurs if the angle of incidence is greater compare to certain limiting angle.
Therefore, option A is correct.
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Suppose that you would like to study star A all year round. Its declination is 25 degrees above the celestial equator. At which of the following locations on Earth could you be to observe this star all year round?
(a) at a latitude of 67 degrees N
(b) only at the South Pole
(c) at a latitude of 63 degrees N
(d) at a latitude of 25 degrees N
Answers
The declination is also known as latitude hence, star A is at a latitude of 25 degrees N from the earth so, option D is correct.
What is the equator?A hypothetical line that would make a large circle around the Earth's surface, equidistant from the poles and on a plane perpendicular to the axis of rotation of the planet, is known as an equator. It establishes the boundary between the Northern and Southern hemispheres of the Earth and serves as the standard for measuring latitude.
Considering that, star A's declination is 25 degrees above the celestial equator. The star is located at a latitude of 25 degrees to the North because the declination is also known as the latitude. Therefore, the observer must be (d) located at a latitude of 25 degrees N in order to examine the star all year long.
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A 9.0-kg box of oranges slides from rest down a frictionless incline from a height of 5.0 m. A constant frictional force, caused by friction with the surface from point A to point B, brings the block to rest at point B, 19 m from point A. What is the coefficient of kinetic friction between A and B?
The gravitational potential energy at the point the box begins must be equal to the kinetic energy at position A and this energy must have been "used up" by friction by the time the box gets to B. So letâs compare the energy at the starting position to that at B (which is zero). There is no reason to include point A.
Answers
When a 9.0-kg box of oranges slides from rest down a frictionless incline from a height of 5.0 m with a frictional force then the coefficient of kinetic friction between A and B is 9.9m/s.
What is kinetic friction?The frictional force acting between two moving objects is termed as Kinetic friction.
Solution:
Given:
Let v represent the speed of the box at point A, x represent the distance the box slides down the slope (without friction), and represent the angle of the incline.
Remember that v = ultimate speed, therefore v 2 - v02 = 2 an x
beginning speed being
A=acceleration and X=displacement
While moving up the slope, the box begins at rest (v0 = 0) and moves a distance x with an acceleration of a to reach a speed v.
F = m g sin() = m a, where m = 9.0 kg and g = 9.8 m/s2, and a = g sin().
Using a little trigonometry, write the distance x in terms of :
x = (5.0 m) / sin(x), where sin(x) = (5.0 m)
To find:v, enter the following into the formula above:
= 2 g sin(5.0 m) / sin(5.0 m)
10.0 m) g v
= 9.9 m/s
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PLEASE HELP ME ANSWER THE PHYSICS QUESTIONS ON MY PROFILE!!! i will give brainliest to the first to answer!!! this one and the other ones
A 2,713 kg van runs into the back of a 843 kg compact car at rest. They move off together at 6.9 m/s. Assuming the friction with the road is negligible, calculate the initial speed of the van.
Answers
Answer:
The initial speed of the van is 9.044 m/s
Explanation:
After an inelastic collision, bodies stick together and move at a common speed. Momentum is conserved, but some kinetic energy is lost.
Here is the formula for an inelastic collision:
[tex]m_1*v_{1i} +m_2*v_{2i}=v_f(m_1+m_2)[/tex]
Let the van be object 1; let the compact car be object 2.
Lets solve for [tex]v_{1i}[/tex]
Isolate terms with [tex]v_{1i}[/tex] to the left hand side.
Subtract [tex]m_2*v_{2i}[/tex] from both sides:
[tex]m_1*v_{1i}=v_f(m_1+m_2)-m_2*v_{2i}[/tex]
Divide both sides by [tex]m_1[/tex].
[tex]v_{1i}=\frac{v_f(m_1+m_2)-m_2*v_{2i}}{m_1}[/tex]
Simplify
[tex]v_{1i}=\frac{m_2(v_f-v_{2i})}{m_1}+v_f[/tex]
Enter our numbers into the equation.
[tex]m_1=2713[/tex]
[tex]m_2=843[/tex]
[tex]v_{2i} =0[/tex]
[tex]v_f=6.9[/tex]
[tex]v_{1i} =\frac{843(6.9-0)}{2713} +6.9[/tex]
[tex]v_{1i} =\frac{843(6.9)}{2713} +6.9[/tex]
[tex]v_{1i} =\frac{5816.7}{2713} +6.9[/tex]
[tex]v_{1i} =2.144 +6.9[/tex]
[tex]v_{1i} =9.044[/tex]
If a piece of elastic wire 2 meters long and 3 centimeters in diameter increases its length by 2.5 cm when a force of 0.25 is applied to its area than Find the force applied on the string and the Young's scale of the string?
Answers
Answer:
The force applied on the string is 0.25 N and the Young's modulus of the string is 10 N/m
Explanation:
The force applied on the string can be calculated using the equation:
Force = (change in length * Young's modulus) / original length
The Young's modulus of the string can be calculated using the equation:
Young's modulus = (Force * original length) / change in length
Plugging in the given values:
Force = (2.5 cm * Young's modulus) / 2 m
= (0.025 m * Young's modulus) / 2 m
= 0.025 * Young's modulus
= 0.25 (given)
= 0.25 N
Young's modulus = (0.25 N * 2 m) / 0.025 m
= 10 N/m
determine the moment with the following data: weight (lb) mom/1000 empty weight 1,350 51.5 pilot and front passenger 340 --- fuel (std tanks) capacity --- oil, 8 qt. --- ---
Answers
Currently, the information is as follows: weight (lb) (lb) mother/1000 empty weight 74.9 pound-inches.
Describe a weight example.In the International System of Units (SI), the newton is used as the unit of measurement for force, which is used to quantify weight. On the surface of the Earth, a one kilogram object weighs around 9.8 newtons, but the weight of the same thing on the Moon is only about one-sixth as great.
The definition of weight in physicsAll things near Earth are constantly under the influence of weight. All things are subject to the gravitational attraction of the Earth, which pushes them all toward its core.
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Consider the AC circuit in the figure. The frequency of the AC source is adjusted while its voltage amplitude is held constant. The lightbulb will glow the brightest at which of the following?
A.high frequencies
B.the brightness will be the same at all frequencies
C.low frequencies
Answers
When the leg it is in has the least resistance, the lightbulb may glow brightest. Because inductive capacitance is inversely proportional to angular frequency, this occurs at low frequencies.
What generates opposition?Electrons moving through a conductors, for example a metal wire, create an electric current. The ions inside the metal may be struck by the speeding electrons. Resistance results this from, making it harder for the current to flow.
A resistance example is what?To better understand resistance, imagine how difficult it would be for a person to move from one shop to the next in a crowded market. This circumstance is undoubtedly comparable to an atom trying to get through a wire.
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for d, you will want to mention a specific term/concept that you're describing for why mrp is downward sloping.
Answers
Inside this services and products (G&S) financial instrument, the DD curve depicts the link between variations through one exogenous construct and one regressor.
What is a MRP?The marginal revenue generated by using one more unit of a product is known as the marginal product of labor (MRP). MRP is used to calculate the ideal resource level while also making crucial decisions about the company's output. The MRP makes the assumption that expenses for other components won't change.
With increased production, a commodity's marginal usefulness decreases. As a result, when there is a greater supply, prices would decrease and demand will rise. Therefore, when the price is lower, consumers would desire fewer things. The aggregate supply slopes downward for this reason.
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the purpose of high voltage direct current transmission lines to decrease the number of conductors needed for transmission of power in a grid system.
Answers
Capacitance is a direct issue with alternating current. The amount of power that may be sent across a line and the minimum distance between lines are both constrained by capacitance between parallel lines.
What does voltage mean, exactly?When charged electrons (current) are forced through a conducting loop by the pressure of an electrical circuit's power source, they may perform tasks like lighting a lamp. In a nutshell, voltage equals pressure and is expressed in volts (V).
What does voltage mean in kid-friendly terms?The difference in electrical energy between two circuit components is known as voltage. It is measured in volts and is measurable with a voltmeter. The current increases as the voltage grows. Higher electrical voltage and current are required for large electrical appliances.
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The amount of work done on an object is the force applied to the object times the distance the object is moved while the force is applied or, more succinctly, work = (force)(distance). We will use the International System of Units: Force is measured in Newtons, N, and distance is measured in meters, m. Weight is the gravitational force applied to the object and cable, therefore, weight = force. Cable (3 N per m) 40 - X Object (1500 N) Ax How much work is done lifting a 1500 N object from the ground to the top of a 40 m building if the cable weighs 3 N per m? Here the 1500 N object is constant, but as you retract the cable, the overall weight (force) decreases. The diagram to the right can help you derive the integral to calculate the work done from the ground to the top of the buildingX1=40X2=0
Answers
The Total work done = work done on the object + work done on the cable
From the given information,
weight of the object is = 1500 N
weight of rope is = 3N per m
height interval is = 0 to 40 m
Work = force x distance
If distance = x, then, we have the integral below as shown in the image:
By substituting x = 40 and x = 0, it becomes
1620(40) - 3/2 * (40)^2 - 1620(0) - 3/2 * (0)^2
= 64800 - 2400
= 62400 Nm
the work done from the ground to the top of the building is 62400 Nm
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In Chapter 9 we will define the center of mass of an object and prove that its motion is described by the particle under constant acceleration model when constant forces act on the object. A gymnast jumps straight up, with her center of mass moving at 2.80 m/s as she leaves the ground. How high above this point is her center of mass (a) 0.100 s , (b) 0.200 s (c) 0.300 s, and (d) 0.500 s thereafter?
Answers
A position established in relation to an object or set of objects is the center of mass. It represents the system's average location as weighted by each component's mass.
The center of mass for straightforward stiff objects with homogeneous density is found at the centroid. The location where the distribution of mass is constant in all directions called the center of mass.
speed of the gymnast = 2.80 m/s
using the second equation of motion,
s = u t + 1/2 a t ^2
the position at time, t = 0.100 sec
s = (2.80) (0.100) + 1/2 (-9.8 m/s^2) (0.100)^2
s = 0.231 m.
the position at time, t = 0.200 sec
s = 0.364 m.
the position at time, t = 0.300 sec
s = 0.399 m.
the position at time, t = 0.500 sec
s = 0.175 m.
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An object is hung from a spring balance attached to the ceiling of an elevator cab. The balance reads 40 N when the elevator is standing still.
(a) What is the reading when the elevator is moving upward with a constant speed of 9.0 m/s?
1 N
(b) What is the reading when the elevator is moving upward with a speed of 9.0 m/s while decelerating at a rate of 1.1 m/s2?
2 N
Answers
(a) The reading when the elevator is moving upward with a constant speed of 9.0 m/s is 40 N.
(b) The reading when the elevator is moving upward with a speed of 9.0 m/s while decelerating at a rate of 1.1 m/s² is 35.11 N.
What is acceleration?
The rate of change in an object's velocity with respect to time is known as acceleration in mechanics. In vector quantities, accelerations exist (in that they have magnitude and direction).
The direction of the net force that is acting on an object determines its acceleration.
According to the given question:
Balance force ( W ) = 40 N
a) moving upward with constant velocity (V ) = 9 m/s.
The reading will not change since it is moving with constant velocity
W = 40 N
b) Moving upward with V = 9 m/s and decelerating at the rate of
(a ) = 1.1 m /s²
The net force ( F ) = W - ma
where m = W/g = 40/9 = 4.45 kg
F = 40 - 4.45 * 1.1 = 35.11 N
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how much work is done when a mass of 3kg (weighing 30N) is lifted vertically through 6m?
Answers
Answer:
180 J is the answer to how much work is done when a mass of 3kg is lifted vertically through 6 m
To calculate the amount of work done when a mass is lifted vertically through a certain distance, we can use the formula:
Work = Force * Distance
In this case, the mass is 3kg, which weighs 30N, and it is lifted vertically through a distance of 6m. Plugging these values into the formula, we get:
Work = 30N * 6m
= 180 Joules
Therefore, the amount of work done when the mass is lifted vertically through 6m is 180 Joules.
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A coffee mug is _____ while a wine glass is _____. Question 6 options: transparent; opaque opaque; transparent translucent; opaque translucent; transparent
Answers
Answer:
A coffee mug is opaque while a wine glass is transparent.
A 3.20 kg fish is attached to the lower end of a vertical spring that has negligible mass and force constant 850 N/m . The spring initially is neither stretched nor compressed. The fish is released from rest.What is its speed after it has descended 0.0490 m from its initial position?
Answers
The speed of the spring from its initial position is 0.8 m/s.
What is the speed of the spring?
The speed of the spring after it descended from the given position is calculated by applying the principle of conservation of energy.
K.E = U
¹/₂mv² = ¹/₂kx²
mv² = kx²
v² = kx² / m
v = √ ( kx² / m )
where;
k is the spring constantx is the extension of the springm is the mass of the fishThe speed of the spring after descending the given distance is calculated as;
v = √ ( 850 x 0.049² / 3.2 )
v = 0.8 m/s
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A bare helium nucleus has two positive charges and a mass of 6.64 ✕ 10−27 kg.
Answers
Answer:
The answer is the question 6.64*10-24=39.4
A 10 kg rock falls from a height of 18 m and
lands on a guy about 3 s later. How much power
did it hit him with?
Answers
It struck him with 60 W of power. when a 10 kg rock hits a guy after falling from a height of 18 m and landing on him after around 3 s.
What does the word "power" mean?Power is the rate of production of work. P=Wt. The watt (W), which is equal to 1 joule per second (1J/s), is the SI unit for power. Power is a measure of how quickly energy is used up since power is the transfer of energy. An example would be a 60-W light bulb, which uses 60 J of energy every second.
Power= mass. velocity + power=10*18/3*10 = 60 W,
resulting in the power of a falling rock being 60W.
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5. Which of the following is true about the Wechsler tests?
O
The Wechsler tests use a number of subtests to measure both verbal and nonverbal intelligence.
The Wechsler tests use a number of subtests to measure emotional intelligence.
The Wechsler tests use a number of subtests to measure eight different types of intelligence.
The Weschler tests can prove a test taker is a savant.
Answers
Answer:
One true statement about the Wechsler tests is that they use a number of subtests to measure both verbal and nonverbal intelligence. The Wechsler Adult Intelligence Scale (WAIS) and the Wechsler Intelligence Scale for Children (WISC) are among the most commonly used intelligence tests in the world. These tests are designed to assess an individual's cognitive abilities, including their ability to think abstractly, solve problems, and understand and use language. The tests use a variety of subtests to measure different aspects of intelligence, including verbal comprehension, perceptual reasoning, working memory, and processing speed. These subtests are combined to produce a full-scale IQ score, which provides an overall measure of an individual's cognitive ability.
What is the displacement illustrated?
What is the distance illustrated?
start/finish
2m
4m
4m
2m
Answers
(a) The displacement of the person as illustrated is 0 m.
(b) The distance travelled by the person is determined as 12 m.
What is the displacement of the person?
The displacement of the person as illustrated is the change in the position of the person.
Mathematically, the formula for displacement of an person is given as;
Δx = xf - xi
where;
xf is the final position of the personxi is the initial position of the personΔx = (2 m + 4m ) - ( 4m + 2m ) = 0
The total distance travelled by the person is calculated as;
d = 2 m + 4 m + 4 m + 2 m
d = 12 m
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