Q: A cyclist of mass $75\ \mathrm{kg}$ climbs a $6.0^\circ$ hill at a constant speed of $4.0\ \mathrm{m/s}$. What is the minimum power output required to overcome gravity (neglecting friction)?

$P = mg \sin(6.0^\circ) \times 4.0$

Question 1

Which of the following best defines power in the context of physics?

Accepted Answer

The rate at which work is done or energy is transferred.

Question 2

A cyclist of mass $75\ \mathrm{kg}$ climbs a $6.0^\circ$ hill at a constant speed of $4.0\ \mathrm{m/s}$. What is the minimum power output required to overcome gravity (neglecting friction)?

Accepted Answer

$P = mg \sin(6.0^\circ) 	imes 4.0$

Question 3

Which unit is equivalent to a Watt ($W$)?

Accepted Answer

$1\ \mathrm{J} / \mathrm{s}$

Question 4

If a $1\ \mathrm{kg}$ ball moving at $10\ \mathrm{m/s}$ hits a wall and comes to rest in $0.002\ \mathrm{s}$, what is the average force exerted by the wall on the ball?

Accepted Answer

$F = 5000\ \mathrm{N}$

Question 5

Which equation correctly relates impulse ($J$) to the change in momentum ($\Delta p$)?

Accepted Answer

$J = \Delta p$

Question 6

A $0.060\ \mathrm{kg}$ ball moving at $5.50\ \mathrm{m/s}$ collides head-on with a $0.090\ \mathrm{kg}$ ball moving in the same direction at $3.00\ \mathrm{m/s}$. If the collision is perfectly elastic, which conservation laws must be applied to solve for the final velocities?

Accepted Answer

Conservation of momentum and conservation of kinetic energy.

Question 7

In a perfectly inelastic collision, which of the following statements is true?

Accepted Answer

The colliding objects stick together after the collision.

Question 8

A car of mass $m$ traveling at velocity $v$ collides and sticks to an identical stationary car. What is their common velocity after the collision?

Accepted Answer

$v' = v/2$

Question 9

Which of the following best describes the Law of Conservation of Momentum?

Accepted Answer

The total momentum of a system remains constant if no external force acts on it.

Question 10

Which formula expresses the relationship between force and the rate of change of momentum?

Accepted Answer

$F = \frac{dp}{dt}$

Question 11

A cyclist moves up a hill at constant speed. Which forces must be considered to calculate the required power output?

Accepted Answer

Both the gravitational force component along the hill and friction.

Question 12

Which of the following is true for an elastic collision?

Accepted Answer

Both momentum and kinetic energy are conserved.

Question 13

A $0.060\ \mathrm{kg}$ ball moving at $5.50\ \mathrm{m/s}$ collides elastically with a $0.090\ \mathrm{kg}$ ball moving at $3.00\ \mathrm{m/s}$ in the same direction. Which equation would you use to find the final velocity of the $0.060\ \mathrm{kg}$ ball?

Accepted Answer

$v_1' = \frac{(m_1 - m_2)v_1 + 2m_2 v_2}{m_1 + m_2}$

Question 14

Which scenario best illustrates the concept of impulse?

Accepted Answer

A tennis ball being struck by a racket, changing its velocity rapidly.

Question 15

If the time of impact during a collision is decreased, what happens to the average force experienced by the object?

Accepted Answer

The average force increases.

Question 16

Which of the following is NOT a requirement for the Law of Conservation of Momentum to hold?

Accepted Answer

The collision is perfectly elastic.

Question 17

A cyclist of mass $75\ \mathrm{kg}$ climbs a $6.0^\circ$ hill at $4.0\ \mathrm{m/s}$, and the total force required is $F$. What is the power output?

Accepted Answer

$P = Fv$

Question 18

Which of the following is a correct statement about mechanical energy in the presence of nonconservative forces?

Accepted Answer

Mechanical energy can change due to work done by nonconservative forces.

Question 19

In a real-world car crash, why is the time of impact important for passenger safety?

Accepted Answer

Increasing the time of impact reduces the average force experienced by passengers.

Question 20

Which of the following best describes the difference between elastic and inelastic collisions?

Accepted Answer

Elastic collisions conserve both momentum and kinetic energy, while inelastic collisions conserve only momentum.

Physics Study Notes: Power, Work, and Momentum

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