Q: A block of mass $$m_2 is on a$$ $$30^ ext{o}$$ inclined plane connected by a string over a pulley to a hanging mass $$m_1. If $$the coefficient of kinetic friction between $$m_2$$ and the plane is $$\mu_k$$, which equation correctly applies Newton's second law to $$m_2$$ along the direction parallel to the incline?

$$m_2 g$$ \sin(30^\text{o}) - T_{S2} = $$m_2 a$

Q: A $$2.0\ \text{kg}$$ block slides up a $$19^\text{o}$$ incline for $$15.0\ \text{m}$$ before coming to rest. If its initial speed is $$5.0\ \text{m/s}$$, what is the correct equation to find the average coefficient of friction $$\mu_k$$?

$$\frac{1}{2}mv_i^2$ = mgd\sin(19^\text{o}) + \mu_k mgd\cos(19^\text{o})$$

Q: A cyclist of mass $$75\ \text{kg}$$ climbs a $$6.0^\text{o}$$ hill at a steady speed of $$4.0\ \text{m/s}. $$What is the minimum power output required to climb the hill, ignoring friction?

$$P = m g \sin(6.0^\text{o}) v$$

Question 1

A block of mass $$m_2 is on a$$ $$30^	ext{o}$$ inclined plane connected by a string over a pulley to a hanging mass $$m_1. If $$the coefficient of kinetic friction between $$m_2$$ and the plane is $$\mu_k$$, which equation correctly applies Newton's second law to $$m_2$$ along the direction parallel to the incline?

Accepted Answer

$$m_2 g$$ \sin(30^	ext{o}) - T_{S2} = $$m_2 a$

Question 2

Which of the following is the correct expression for the work done by a spring with spring constant $$k$$ when compressed by a distance $$x$$ from its equilibrium position?

Accepted Answer

$$W = \frac{1}{2}kx^2$

Question 3

A 0.185 kg block is placed against a spring with $$k = 360\ 	ext{N/m}$$ and compressed by $$x = 0.110\ 	ext{m}. $$What is the maximum speed of the block when released from rest?

Accepted Answer

$$v = \sqrt{\frac{kx^2$}{m}}$$

Question 4

Which of the following statements about conservative forces is correct?

Accepted Answer

Conservative forces depend only on the initial and final positions.

Question 5

A roller coaster car of mass $$m$$ starts from rest at the top of a $$40.0\ 	ext{m}$$ hill. Ignoring friction, what is its speed at the bottom of the hill?

Accepted Answer

$$v = \sqrt{2gh}$$

Question 6

A person jumps from a platform with a vertical speed of $$4.5\ 	ext{m/s}$$ onto a trampoline $$2.0\ 	ext{m}$$ below. The trampoline behaves like a spring with $$k = 5.8 	imes 10^4$\ 	ext{N/m}. $$What is the equation relating the compression $$y of $$the trampoline to the initial energy?

Accepted Answer

$$\frac{1}{2}mv_i^2$ + mgy = \frac{1}{2}ky^2$

Question 7

Which of the following is the correct statement of the principle of conservation of mechanical energy for a system with only conservative forces?

Accepted Answer

$$K_i + U_i = K_f + U_f$$

Question 8

A $$0.5\ 	ext{kg}$$ object falls from a height of $$10\ 	ext{m} to $$the ground. What is its speed just before hitting the ground? (Ignore air resistance.)

Accepted Answer

$$v = \sqrt{2gh}$$

Question 9

A $$2.0\ 	ext{kg}$$ block slides up a $$19^	ext{o}$$ incline for $$15.0\ 	ext{m}$$ before coming to rest. If its initial speed is $$5.0\ 	ext{m/s}$$, what is the correct equation to find the average coefficient of friction $$\mu_k$$?

Accepted Answer

$$\frac{1}{2}mv_i^2$ = mgd\sin(19^	ext{o}) + \mu_k mgd\cos(19^	ext{o})$$

Question 10

Which of the following is the correct formula for power in terms of force and velocity?

Accepted Answer

$$P = Fv$$

Question 11

A cyclist of mass $$75\ 	ext{kg}$$ climbs a $$6.0^	ext{o}$$ hill at a steady speed of $$4.0\ 	ext{m/s}. $$What is the minimum power output required to climb the hill, ignoring friction?

Accepted Answer

$$P = m g \sin(6.0^	ext{o}) v$$

Question 12

Which of the following is NOT a form of potential energy discussed in the course?

Accepted Answer

Chemical potential energy

Question 13

If nonconservative forces (like friction) are present, which equation correctly relates the change in kinetic energy, potential energy, and work done by nonconservative forces?

Accepted Answer

$$\Delta K + \Delta U = W_{nc}$$

Question 14

A spring with $$k = 360\ 	ext{N/m} is $$compressed by $$0.110\ 	ext{m}. $$How much potential energy is stored in the spring?

Accepted Answer

$$U = \frac{1}{2}kx^2$

Question 15

Which of the following best describes the direction of the restoring force in a spring according to Hooke's Law?

Accepted Answer

The restoring force always acts opposite to the direction of stretch or compression.

Question 16

A rock is dropped from a height of $$30\ 	ext{m}$$ and reaches $$10\ 	ext{m}$$ above the ground. What is its velocity at $$10\ 	ext{m}$$?

Accepted Answer

$$v = \sqrt{2g(h_1$ - h_2$)}$$

Question 17

Which of the following is true about mechanical energy in a system with only conservative forces?

Accepted Answer

Mechanical energy remains constant.

Question 18

Which of the following is the correct unit for power?

Accepted Answer

Watt ($$	ext{W})$$

Newton’s Laws and Energy Conservation: Inclined Plane and Pulley Systems

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