Question 1

In an elastic collision,

Accepted Answer

In an elastic collision, kinetic energy is conserved. Momentum is also conserved in all collisions, whether they are elastic or inelastic. Therefore, options A and D are incorrect. Option B is incorrect because although kinetic energy is not conserved in an inelastic collision, it is conserved in an elastic collision.

Question 2

An empty railroad car traveling at a speed of 21 m/s strikes a second car at rest.The second car,being full with passengers,has twice the mass of the first car.If the cars lock together as a result of the collision,their common speed afterward is

Accepted Answer

E

Question 3

The sum of the forces acting on an object is equal to

Accepted Answer

This is Newton's second law - the sum of the forces on an object is equal to the rate of change of its momentum. While impulse can cause a change in momentum, it is the sum of the forces that lead to that change. Therefore, A and B are incorrect choices. Option D is not correct as well, since C is the correct answer.

Question 4

Astronauts are playing baseball on the International Space Station.One astronaut with a mass of 60.0 kg,initially at rest,hits a baseball with a bat.The baseball was initially coming toward the astronaut at 30.0 m/s and after the ball is hit,the ball travels in the opposite direction with a speed of 50.0 m/s.The mass of a baseball is 0.120 kg.The recoil velocity of the astronaut is

Accepted Answer

Using the conservation of momentum, the initial momentum of the system is the momentum of the baseball: (0.120 kg)(30.0 m/s). The final momentum is the sum of the momentum of the baseball and the astronaut. Solving for the astronaut's velocity gives 0.160 m/s.

Question 5

Particle one of mass m initially moves to the right at v.Particle two of mass 2m is initially at rest.After they undergo an elastic collision,particle one moves directly down.What is the final speed of particle two?

Accepted Answer

Momentum is conserved in the x direction, so the total momentum before the collision is mv to the right, and the total momentum after the collision is 2mv to the left. Therefore, the x component of the velocity of particle two after the collision is -v/2.Kinetic energy is also conserved in the collision, so the total kinetic energy before the collision is 1/2 mv^2, and the total kinetic energy after the collision is 1/2 (2m)v^2/4 + 1/2 mv^2/4 = 3/4 mv^2. Therefore, the speed of particle two after the collision is sqrt(3/4) v = 0.577 v.

Question 6

An object initially at rest explodes into three pieces,each of which has the same mass.Piece one moves north and piece two moves east.Which piece has the largest speed?

Accepted Answer

Since the object initially was at rest, its initial momentum was zero. To conserve momentum, the vector sum of the momenta of the three pieces must also be zero. If pieces one and two move perpendicular to each other (north and east), the third piece must move in the opposite direction to the vector sum of the first two pieces to balance the momentum. Given that all pieces have the same mass, for the momentum vectors to cancel out, the speed of the third piece must be larger than the speed of the first two pieces, as it has to counteract the combined momentum of the other two.

Question 7

Particle one of mass m initially moves to the right at v.Particle two of mass 3m is initially at rest.After they undergo an elastic collision,particle one moves directly down.In what direction does particle two move relative to the initial direction of particle one?

Accepted Answer

The answer of Particle one of mass m initially moves...

Question 8

A 0.280-kg ball makes an elastic head-on collision with a second ball initially at rest.The second ball moves off with one fourth the original speed of the first ball.What is the velocity of the first ball after the collision,in terms of its initial velocity,v?

Accepted Answer

The answer of A 0.280-kg ball makes an elastic head-on...

Question 9

An SUV of mass 2200 kg,moving with a speed of 35 m/s on the highway,passes a car with the mass 1500 kg and a kinetic energy equal to that of the SUV.The ratio of the momentum of the car relative to that of the SUV is

Accepted Answer

The kinetic energy of an object can be calculated as:

K = 1/2 * m * v^2

where,
K = kinetic energy
m = mass of the object
v = velocity of the object

Let the velocity of the car be v2 and its momentum be p2.

Given:
mass of SUV, m1 = 2200 kg
velocity of SUV, v1 = 35 m/s
mass of car, m2 = 1500 kg
kinetic energy of car = kinetic energy of SUV

Therefore,

1/2 * m1 * v1^2 = 1/2 * m2 * v2^2

v2 = sqrt(m1/m2) * v1

p1 = m1 * v1
p2 = m2 * v2 = m2 * (sqrt(m1/m2) * v1) = sqrt(m1 * m2) * v1

Ratio of momentum of car to that of SUV
p2/p1 = sqrt(m1 * m2) * v1 / (m1 * v1) = sqrt(m2/m1) = sqrt(1500/2200) = 0.83

Therefore, the ratio of momentum of the car to that of the SUV is 0.83. Answer choice B is correct.

Question 10

I run toward the wall at 5.00 m/sec to the left.My mass is 90.0 kg.I collide with the wall and come to rest in 0.100 sec.What was the average normal force on my body due to the wall?

Accepted Answer

The average normal force can be calculated using the change in momentum over time, which is essentially the mass times the change in velocity divided by the time interval. The initial velocity is 5.00 m/s to the left (we can consider this as -5.00 m/s for calculation purposes), and the final velocity is 0 m/s (since the person comes to rest). The change in velocity is therefore 5.00 m/s. Using the formula for force, $ F = \frac{m \Delta v}{\Delta t} $, where $ m = 90.0 \, \text{kg} $, $ \Delta v = 5.00 \, \text{m/s} $, and $ \Delta t = 0.100 \, \text{s} $, we get $ F = \frac{90.0 \times 5.00}{0.100} = 4500 \, \text{N} $.

Question 11

An SUV of mass 2200 kg,moving with a speed of 35 m/s on the highway,passes a car with the mass 1500 kg and a kinetic energy equal to that of the SUV.The ratio of the momentum of the SUV relative to that of the car is

Accepted Answer

The answer of An SUV of mass 2200 kg,moving with...

Question 12

An SUV of mass 2200 kg,moving with a speed of 35 m/s on the highway,passes a car with the mass 1500 kg and a linear momentum equal to that of the SUV.The ratio of the kinetic energy of the SUV relative to that of the car is

Accepted Answer

The answer of An SUV of mass 2200 kg,moving with...

Question 13

A 1000-kg car is travelling west at 17.0 m/s toward an intersection.A 1500-kg truck is travelling north at 20.0 m/s toward the same intersection.The car and truck collide at the intersection and stick together.What is their speed after the collision?

Accepted Answer

The speed after the collision can be found using the conservation of momentum. The total momentum before the collision is equal to the total momentum after the collision. The momentum of each vehicle before the collision is given by $p = mv$, where $m$ is the mass and $v$ is the velocity. The total momentum in the x-direction (west-east) before the collision is $p_{x,car} = (1000\,kg)(-17.0\,m/s)$ (negative because it's west), and in the y-direction (north-south), it's $p_{y,truck} = (1500\,kg)(20.0\,m/s)$. After the collision, the car and truck move together with a combined mass of $2500\,kg$ and a velocity $v$ at an angle $\theta$ to the north. The magnitude of the velocity can be found using the Pythagorean theorem, $v = \sqrt{v_x^2 + v_y^2}$, where $v_x$ and $v_y$ are the velocities in the x and y directions, respectively. Substituting the values, $v = \sqrt{(-17.0)^2 + 20.0^2} = 13.8\,m/s$.

Question 14

A 1000-kg car is travelling west at 17.0 m/s toward an intersection.A 1500-kg truck is travelling north at 20.0 m/s toward the same intersection.The car and truck collide at the intersection and stick together.What is the final kinetic energy of the system?

Accepted Answer

The initial kinetic energy of the car is 0.5 x 1000 kg x (17.0 m/s)^2 = 1.44 x 10^5 J
The initial kinetic energy of the truck is 0.5 x 1500 kg x (20.0 m/s)^2 = 3.00 x 10^5 J
The total initial kinetic energy is 1.44 x 10^5 J + 3.00 x 10^5 J = 4.44 x 10^5 J
Since the car and truck stick together after the collision, the final velocity of the combined system can be found using conservation of momentum.
The initial momentum of the system is (1000 kg x 17.0 m/s) + (1500 kg x 20.0 m/s) = 45500 kg*m/s + 30000 kg*m/s = 75500 kg*m/s
Since momentum is conserved, the final momentum of the system is also 75500 kg*m/s.
The combined mass of the car and truck is 1000 kg + 1500 kg = 2500 kg.
Therefore, the final velocity of the system is 75500 kg*m/s ÷ 2500 kg = 30.2 m/s
The final kinetic energy of the system is 0.5 x 2500 kg x (30.2 m/s)^2 = 2.28 x 10^6 J
Subtracting the initial kinetic energy from the final kinetic energy gives the change in kinetic energy, which is the answer to the question: 2.28 x 10^6 J - 4.44 x 10^5 J = 1.84 x 10^6 J
Rounding to 3 significant figures gives 2.38 x 10^6 J, which is choice C.

Question 15

A child in a sled is moving with a speed of 4.0 m/s across an iced over pond.If the total mass of the sled-child system is 85.0 kg,what magnitude of the average force is required to bring the sled to rest in 10.0 s?

Accepted Answer

To bring the sled to rest, we need to calculate the deceleration and then use Newton's second law to find the force. The initial velocity (v_i) is 4.0 m/s, and the final velocity (v_f) is 0 m/s (since the sled comes to rest), over a time (t) of 10.0 s. The deceleration (a) can be found using the formula $a = \frac{v_f - v_i}{t}$. Plugging in the values, $a = \frac{0 - 4.0}{10.0} = -0.4 \, m/s^2$. The negative sign indicates deceleration. The force required can be found using Newton's second law, $F = ma$, where $m$ is the mass and $a$ is the acceleration (or in this case, deceleration). The mass (m) is 85.0 kg, and the acceleration (a) is -0.4 m/s^2. Thus, $F = 85.0 \times -0.4 = -34 \, N$. The negative sign indicates the direction of the force is opposite to the motion, but since the question asks for the magnitude, we take the absolute value, which is 34 N.

Question 16

An SUV of mass 2200 kg,moving with a speed of 35 m/s on the highway,passes a car with the mass 1500 kg and a linear momentum equal to that of the SUV.The ratio of the kinetic energy of the car relative to that of the SUV is

Accepted Answer

The linear momentum of both the SUV and the car is equal. The formula for linear momentum ($p$) is $p = mv$, where $m$ is mass and $v$ is velocity. Since their momentums are equal, we have $2200 \times 35 = 1500 \times v_{\text{car}}$, solving for $v_{\text{car}}$ gives us $v_{\text{car}} = \frac{2200 \times 35}{1500}$. The kinetic energy ($KE$) formula is $KE = \frac{1}{2}mv^2$. The ratio of the car's kinetic energy to the SUV's kinetic energy is $\frac{\frac{1}{2} \times 1500 \times (\frac{2200 \times 35}{1500})^2}{\frac{1}{2} \times 2200 \times 35^2}$, which simplifies to $\frac{1500}{2200} \times (\frac{2200}{1500})^2$, further simplifying to $\frac{2200^2}{1500^2}$, which equals $\frac{2200}{1500}$ (since the $\frac{1}{2}$ and $35^2$ cancel out). This gives a ratio of $\frac{2200}{1500}$ which simplifies to $\frac{22}{15}$, approximately equal to 1.47.

Question 17

A 0.280-kg ball makes an elastic head-on collision with a second ball initially at rest.The second ball moves off with one fourth the original speed of the first ball.The mass of the second ball is

Accepted Answer

The answer of A 0.280-kg ball makes an elastic head-on...

Question 18

Consider two carts,of masses m and 2m,at rest on a frictionless air track.You push the first cart for 3 s and then the other for the same length of time and with the same force.The final speed of the cart with mass 2 m is

Accepted Answer

According to Newton's second law, F = ma. Since both carts experience the same force and are initially at rest, the acceleration of the two carts will be the same. Therefore, the final velocity of each cart will depend on their masses and the time they were pushed. Using the equation vf = vi + at, where vi is the initial velocity (zero) and a is the acceleration, we can derive the formula vf = at. Since the carts experience the same force and have the same acceleration but different masses, the cart with mass 2m will have half the acceleration of the cart with mass m. Therefore, the final velocity of the cart with mass 2m will be half the final velocity of the cart with mass m, or one half the speed of the cart of mass m.

Question 19

A 1000-kg car is travelling west at 17.0 m/s toward an intersection.A 1500-kg truck is travelling north at 20.0 m/s toward the same intersection.The car and truck collide at the intersection and sick together.What is the angle of their velocity after the collision relative to the east direction?

Accepted Answer

The answer of A 1000-kg car is travelling west at...

Question 20

Particle one of mass m initially moves to the right at v.Particle two of mass 4m is initially at rest.After they undergo an elastic collision,particle one moves directly down.What is the final speed of particle one?

Accepted Answer

The answer of Particle one of mass m initially moves...

Quiz 7: Momentum and Collisions

In an elastic collision,

An empty railroad car traveling at a speed of 21 m/s strikes a second car at rest.The second car,being full with passengers,has twice the mass of the first car.If the cars lock together as a result of the collision,their common speed afterward is

The sum of the forces acting on an object is equal to

Particle one of mass m initially moves to the right at v.Particle two of mass 2m is initially at rest.After they undergo an elastic collision,particle one moves directly down.What is the final speed of particle two?

An object initially at rest explodes into three pieces,each of which has the same mass.Piece one moves north and piece two moves east.Which piece has the largest speed?

Particle one of mass m initially moves to the right at v.Particle two of mass 3m is initially at rest.After they undergo an elastic collision,particle one moves directly down.In what direction does particle two move relative to the initial direction of particle one?

A 0.280-kg ball makes an elastic head-on collision with a second ball initially at rest.The second ball moves off with one fourth the original speed of the first ball.What is the velocity of the first ball after the collision,in terms of its initial velocity,v?

An SUV of mass 2200 kg,moving with a speed of 35 m/s on the highway,passes a car with the mass 1500 kg and a kinetic energy equal to that of the SUV.The ratio of the momentum of the car relative to that of the SUV is

I run toward the wall at 5.00 m/sec to the left.My mass is 90.0 kg.I collide with the wall and come to rest in 0.100 sec.What was the average normal force on my body due to the wall?

An SUV of mass 2200 kg,moving with a speed of 35 m/s on the highway,passes a car with the mass 1500 kg and a kinetic energy equal to that of the SUV.The ratio of the momentum of the SUV relative to that of the car is

An SUV of mass 2200 kg,moving with a speed of 35 m/s on the highway,passes a car with the mass 1500 kg and a linear momentum equal to that of the SUV.The ratio of the kinetic energy of the SUV relative to that of the car is

A 1000-kg car is travelling west at 17.0 m/s toward an intersection.A 1500-kg truck is travelling north at 20.0 m/s toward the same intersection.The car and truck collide at the intersection and stick together.What is their speed after the collision?

A 1000-kg car is travelling west at 17.0 m/s toward an intersection.A 1500-kg truck is travelling north at 20.0 m/s toward the same intersection.The car and truck collide at the intersection and stick together.What is the final kinetic energy of the system?

A child in a sled is moving with a speed of 4.0 m/s across an iced over pond.If the total mass of the sled-child system is 85.0 kg,what magnitude of the average force is required to bring the sled to rest in 10.0 s?

An SUV of mass 2200 kg,moving with a speed of 35 m/s on the highway,passes a car with the mass 1500 kg and a linear momentum equal to that of the SUV.The ratio of the kinetic energy of the car relative to that of the SUV is

A 0.280-kg ball makes an elastic head-on collision with a second ball initially at rest.The second ball moves off with one fourth the original speed of the first ball.The mass of the second ball is

Consider two carts,of masses m and 2m,at rest on a frictionless air track.You push the first cart for 3 s and then the other for the same length of time and with the same force.The final speed of the cart with mass 2 m is

A 1000-kg car is travelling west at 17.0 m/s toward an intersection.A 1500-kg truck is travelling north at 20.0 m/s toward the same intersection.The car and truck collide at the intersection and sick together.What is the angle of their velocity after the collision relative to the east direction?

Particle one of mass m initially moves to the right at v.Particle two of mass 4m is initially at rest.After they undergo an elastic collision,particle one moves directly down.What is the final speed of particle one?