Q: A 2 kg fish swimming at 3 m/s swallows a stationary 1 kg fish. What is the velocity of the combined fish immediately after the event? (Assume the collision is perfectly inelastic and occurs in one dimension.)

$$v = \frac{2 \times 3 + 1 \times 0}{2 + 1} = 2\ \mathrm{m/s}$$

Q: A 0.5 kg ball is dropped from a height of 10 m. Ignoring air resistance, what is its velocity just before it hits the ground? (Use $$g = 9.8\ \mathrm{m/s^2$})$$

$$v = \sqrt{2gh} = \sqrt{2 \times 9.8 \times 10} = 14\ \mathrm{m/s}$$

Q: A 60 kg acrobat jumps from a platform 5 m high. What is the acrobat's potential energy at the top, and what is their kinetic energy just before landing? (Assume $$g = 9.8\ \mathrm{m/s^2$}$$ and ignore air resistance.)

Potential energy at top: $$PE = mgh = 60 \times 9.8 \times 5 = 2940\ \mathrm{J}$$; Kinetic energy before landing: $$KE = 2940\ \mathrm{J}$$

Q: A 5 kg object is moving at 4 m/s. What is its kinetic energy?

$$KE = \frac{1}{2}mv^2$ = \frac{1}{2} \times 5 \times 16 = 40\ \mathrm{J}$$

Q: Two ice skaters, one with mass 50 kg and the other with mass 70 kg, push off from each other and move in opposite directions. If the 50 kg skater moves at 3 m/s, what is the velocity of the 70 kg skater?

$$v = -\frac{50 \times 3}{70} = -2.14\ \mathrm{m/s}$$

Question 1

A 2 kg fish swimming at 3 m/s swallows a stationary 1 kg fish. What is the velocity of the combined fish immediately after the event? (Assume the collision is perfectly inelastic and occurs in one dimension.)

Accepted Answer

$$v = \frac{2 	imes 3 + 1 	imes 0}{2 + 1} = 2\ \mathrm{m/s}$$

Question 2

Which of the following best describes the law of conservation of momentum in a closed system?

Accepted Answer

The total momentum before an interaction is equal to the total momentum after the interaction.

Question 3

A 0.5 kg ball is dropped from a height of 10 m. Ignoring air resistance, what is its velocity just before it hits the ground? (Use $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$v = \sqrt{2gh} = \sqrt{2 	imes 9.8 	imes 10} = 14\ \mathrm{m/s}$$

Question 4

Which statement about kinetic and potential energy is correct?

Accepted Answer

Kinetic energy is the energy of motion, while potential energy is stored due to position or configuration.

Question 5

A 60 kg acrobat jumps from a platform 5 m high. What is the acrobat's potential energy at the top, and what is their kinetic energy just before landing? (Assume $$g = 9.8\ \mathrm{m/s^2$}$$ and ignore air resistance.)

Accepted Answer

Potential energy at top: $$PE = mgh = 60 	imes 9.8 	imes 5 = 2940\ \mathrm{J}$$; Kinetic energy before landing: $$KE = 2940\ \mathrm{J}$$

Question 6

Which of the following scenarios best illustrates the work-kinetic energy theorem?

Accepted Answer

A person pushes a sled across ice, and the work done equals the change in the sled's kinetic energy.

Question 7

A 5 kg object is moving at 4 m/s. What is its kinetic energy?

Accepted Answer

$$KE = \frac{1}{2}mv^2$ = \frac{1}{2} 	imes 5 	imes 16 = 40\ \mathrm{J}$$

Question 8

In a ballistic pendulum experiment, a bullet of mass 0.02 kg is fired into a 2 kg block suspended from a string. The block and bullet rise to a height of 0.05 m. What was the initial speed of the bullet? (Assume all energy is conserved after collision.)

Accepted Answer

$$v = \frac{(m + M)}{m} \sqrt{2gh} = \frac{2.02}{0.02} \sqrt{2 	imes 9.8 	imes 0.05} \approx 101 	imes 0.99 = 99.99\ \mathrm{m/s}$$

Question 9

Which of the following is true about machines and energy?

Accepted Answer

Machines can multiply force but cannot create energy; the total energy output cannot exceed the energy input.

Question 10

Two ice skaters, one with mass 50 kg and the other with mass 70 kg, push off from each other and move in opposite directions. If the 50 kg skater moves at 3 m/s, what is the velocity of the 70 kg skater?

Accepted Answer

$$v = -\frac{50 	imes 3}{70} = -2.14\ \mathrm{m/s}$$

Question 11

Which of the following best describes an elastic collision?

Accepted Answer

Both momentum and kinetic energy are conserved.

Question 12

A machine has an efficiency of 40%. If you input 500 J of energy, how much useful work does the machine perform?

Accepted Answer

$$W = 0.4 	imes 500 = 200\ \mathrm{J}$$

Question 13

Which equation correctly expresses the work-kinetic energy theorem?

Accepted Answer

$$W = \Delta KE = KE_{final} - KE_{initial}$$

Question 14

A 3 kg cart moving at 2 m/s collides with a stationary 2 kg cart. After the collision, the 3 kg cart moves at 1 m/s. What is the velocity of the 2 kg cart after the collision? (Assume a perfectly elastic collision.)

Accepted Answer

$$3 	imes 2 + 2 	imes 0 = 3 	imes 1 + 2 	imes v$$; $$6 = 3 + 2v$$; $$2v = 3$$; $$v = 1.5\ \mathrm{m/s}$$

Question 15

Which of the following is a real-world example of the conservation of energy?

Accepted Answer

A roller coaster car at the top of a hill has maximum potential energy, which is converted to kinetic energy as it descends.

Question 16

A 10 kg box is lifted vertically 2 m. How much work is done against gravity? (Use $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$W = mgh = 10 	imes 9.8 	imes 2 = 196\ \mathrm{J}$$

Question 17

Which of the following statements about inelastic collisions is correct?

Accepted Answer

Momentum is conserved, but kinetic energy is not.

Question 18

A 0.1 kg ball moving at 5 m/s collides with a 0.2 kg ball at rest. After the collision, the 0.1 kg ball moves at 2 m/s. What is the velocity of the 0.2 kg ball after the collision? (Assume momentum is conserved.)

Accepted Answer

$$0.1 	imes 5 = 0.1 	imes 2 + 0.2 	imes v$$; $$0.5 = 0.2 + 0.2v$$; $$0.2v = 0.3$$; $$v = 1.5\ \mathrm{m/s}$$

Question 19

Which of the following best explains why energy is not created or destroyed in a closed system?

Accepted Answer

Energy can be transformed from one form to another, but the total amount remains constant.

Conservation Laws in Physics: Momentum and Energy

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