Q: Given the sphere in the previous question, what is the net force acting towards the center of the circle?

$$F_{net} = m a_c = 0.50 \times 75.3 = 37.65\ \mathrm{N}$$

Q: A wooden block A of mass 7.0 kg slides on a table when pulled by a hanging block B of mass 7.0 kg. The coefficient of kinetic friction is 0.20. What is the frictional force acting on block A?

$$f_k = \mu_k m_A g = 0.20 \times 7.0 \times 9.8 = 13.72\ \mathrm{N}$$

Q: After the elastic collision described above, how high does the pendulum bob rise above the table?

$$h = \frac{v^2$}{2g} = \frac{0.625^2$}{2 \times 9.8} = 0.02\ \mathrm{m} = 2.0\ \mathrm{cm}$$

Q: A 0.50 kg sphere is tied to two wires and revolves in a horizontal circle. If the tensions in the wires are 27 N and 17 N, what is the total upward force provided by the wires?

$$F_{up} = 27 \sin 30^\circ + 17 \sin 30^\circ = (27 + 17) \times 0.5 = 22\ \mathrm{N}$$

Question 1

A 0.50 kg sphere revolves in a horizontal circle at a constant speed of 8.0 m/s, tied by two wires at 30° angles as shown. What is the centripetal acceleration of the sphere?

Accepted Answer

$$a_c = \frac{v^2$}{r} = \frac{8.0^2$}{0.85} = 75.3\ \mathrm{m/s^2$}$$

Question 2

Given the sphere in the previous question, what is the net force acting towards the center of the circle?

Accepted Answer

$$F_{net} = m a_c = 0.50 	imes 75.3 = 37.65\ \mathrm{N}$$

Question 3

A wooden block A of mass 7.0 kg slides on a table when pulled by a hanging block B of mass 7.0 kg. The coefficient of kinetic friction is 0.20. What is the frictional force acting on block A?

Accepted Answer

$$f_k = \mu_k m_A g = 0.20 	imes 7.0 	imes 9.8 = 13.72\ \mathrm{N}$$

Question 4

In the block and pulley system, if the acceleration of block A is twice that of block B, what is the acceleration of block B if block A accelerates at $$2.4\ \mathrm{m/s^2$}$$?

Accepted Answer

$$a_B = \frac{a_A}{2} = \frac{2.4}{2} = 1.2\ \mathrm{m/s^2$}$$

Question 5

A 0.25 kg block slides at $$1.25\ \mathrm{m/s}$$ and collides elastically with a 0.75 kg pendulum bob hanging from a $$0.45\ \mathrm{m}$$ string. What is the velocity of the pendulum bob immediately after the collision?

Accepted Answer

$$v_{bob} = \frac{2 m_{block}}{m_{block} + m_{bob}} v_{block} = \frac{2 	imes 0.25}{0.25 + 0.75} 	imes 1.25 = 0.625\ \mathrm{m/s}$$

Question 6

After the elastic collision described above, how high does the pendulum bob rise above the table?

Accepted Answer

$$h = \frac{v^2$}{2g} = \frac{0.625^2$}{2 	imes 9.8} = 0.02\ \mathrm{m} = 2.0\ \mathrm{cm}$$

Question 7

A 200 g hockey puck slides at $$3.3\ \mathrm{m/s}$$ and encounters a 20-cm sticky spot, emerging at $$1.4\ \mathrm{m/s}. $$What is the work done by friction?

Accepted Answer

$$W = \Delta K = \frac{1}{2} m (v_f^2$ - v_i^2$) = \frac{1}{2} 	imes 0.2 	imes (1.4^2$ - 3.3^2$) = -0.92\ \mathrm{J}$$

Question 8

For the hockey puck above, what is the magnitude of the friction force experienced while it traveled through the sticky spot?

Accepted Answer

$$F = \frac{|W|}{d} = \frac{0.92}{0.20} = 4.6\ \mathrm{N}$$

Question 9

Which equation correctly expresses Newton's Second Law for a system of forces?

Accepted Answer

$$F_{net} = \sum F_i = m a$$

Question 10

Which formula gives the impulse delivered to an object by a force $$F(t)$$ over a time interval $$t_1 to$$ $$t_2$$?

Accepted Answer

$$J = \int_{t_1$}^{t_2$} F(t) dt$$

Question 11

A ball of mass $$m is $$dropped from height $$h. $$What is its velocity just before hitting the ground, neglecting air resistance?

Accepted Answer

$$v = \sqrt{2 g h}$$

Question 12

Which of the following correctly expresses the work-energy theorem?

Accepted Answer

$$\Delta K = W_{net}$$

Question 13

A 0.50 kg sphere is tied to two wires and revolves in a horizontal circle. If the tensions in the wires are 27 N and 17 N, what is the total upward force provided by the wires?

Accepted Answer

$$F_{up} = 27 \sin 30^\circ + 17 \sin 30^\circ = (27 + 17) 	imes 0.5 = 22\ \mathrm{N}$$

Question 14

In an elastic collision between two masses $$m_1$$ and $$m_2 ($$with $$m_2$$ initially at rest), what is the final velocity of $$m_2$$?

Accepted Answer

$$v_{2f} = \frac{2 m_1$}{m_1$ + m_2$} v_{1i}$$

Question 15

A block slides down a frictionless incline and collides elastically with a stationary block. Which conservation law(s) apply during the collision?

Accepted Answer

Both conservation of momentum and conservation of kinetic energy

Question 16

A force $$F$$ acts on a mass $$m$$ over a distance $$d. $$What is the work done by the force?

Accepted Answer

$$W = F d$$

Question 17

A block of mass $$m$$ slides on a table with friction coefficient $$\mu_k. $$What is the acceleration of the block due to friction?

Accepted Answer

$$a = -\mu_k g$$

Question 18

A pendulum bob of mass $$m$$ rises to height $$h$$ after a collision. What is its change in gravitational potential energy?

Accepted Answer

$$\Delta U = m g h$$

Physics I: Dynamics, Energy, and Collisions – Exam Study Guide

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