Q: A block of mass $$8.0\ \mathrm{kg}$$ hangs from the ceiling by two ropes at angles $$45^\circ$$ and $$25^\circ to $$the horizontal. What is the tension in the rope at $$45^\circ$$? (Assume equilibrium and $$g = 9.8\ \mathrm{m/s^2$}.)$$

$$T_{45} = \dfrac{8.0 \times 9.8 \times \sin 25^\circ}{\sin 45^\circ \sin 25^\circ + \sin^2$ 25^\circ}$$

Q: Suzie pulls a sled of mass $$m at an $$angle $$\theta$$ above the horizontal. If the sled moves at constant velocity and the coefficient of kinetic friction is $$\mu_k$$, what is the tension $$T in $$the rope?

$$T = \mu_k m g / (\cos \theta)$$

Q: A hockey puck of mass $$50.0\ \mathrm{g} is $$moving east at $$2.00\ \mathrm{m/s}$$ when it receives a $$3.00\ \mathrm{N}$$ kick north for $$30.0\ \mathrm{ms}. $$What is the puck's velocity just after the kick?

$$v = \sqrt{2.00^2$ + (3.00 \times 0.030 / 0.050)^2$}\ \mathrm{m/s}$$

Q: A person of mass $$60\ \mathrm{kg}$$ stands on a scale in an elevator accelerating upward at $$2.0\ \mathrm{m/s^2$}. $$What does the scale read?

$$60 \times (9.8 + 2.0)\ \mathrm{N}$$

Q: A box slides down a ramp of length $$d$$ and angle $$\theta$$ with coefficient of kinetic friction $$\mu_k. $$Starting from rest, what is its speed at the bottom?

$$v = \sqrt{2 g d (\sin \theta - \mu_k \cos \theta)}$$

Question 1

A block of mass $$8.0\ \mathrm{kg}$$ hangs from the ceiling by two ropes at angles $$45^\circ$$ and $$25^\circ to $$the horizontal. What is the tension in the rope at $$45^\circ$$? (Assume equilibrium and $$g = 9.8\ \mathrm{m/s^2$}.)$$

Accepted Answer

$$T_{45} = \dfrac{8.0 	imes 9.8 	imes \sin 25^\circ}{\sin 45^\circ \sin 25^\circ + \sin^2$ 25^\circ}$$

Question 2

Suzie pulls a sled of mass $$m at an $$angle $$	heta$$ above the horizontal. If the sled moves at constant velocity and the coefficient of kinetic friction is $$\mu_k$$, what is the tension $$T in $$the rope?

Accepted Answer

$$T = \mu_k m g / (\cos 	heta)$$

Question 3

A box of mass $$m$$ sits at rest on a frictionless incline of angle $$\beta. $$What is the tension in the rope keeping it from sliding down?

Accepted Answer

$$T = m g \sin \beta$$

Question 4

A hockey puck of mass $$50.0\ \mathrm{g} is $$moving east at $$2.00\ \mathrm{m/s}$$ when it receives a $$3.00\ \mathrm{N}$$ kick north for $$30.0\ \mathrm{ms}. $$What is the puck's velocity just after the kick?

Accepted Answer

$$v = \sqrt{2.00^2$ + (3.00 	imes 0.030 / 0.050)^2$}\ \mathrm{m/s}$$

Question 5

Which statement best describes apparent weightlessness experienced in free fall?

Accepted Answer

The normal/support force is zero.

Question 6

A person of mass $$60\ \mathrm{kg}$$ stands on a scale in an elevator accelerating upward at $$2.0\ \mathrm{m/s^2$}. $$What does the scale read?

Accepted Answer

$$60 	imes (9.8 + 2.0)\ \mathrm{N}$$

Question 7

In an Atwood machine with $$m_1$$ \u003e $$m_2$$, what is the acceleration of the system (neglecting friction and mass of the pulley)?

Accepted Answer

$$a = \dfrac{m_1$ - m_2$}{m_1$ + m_2$} g$$

Question 8

A wooden box sits on a wooden ramp. As the ramp's angle increases, at what angle $$	heta$$ will the box start to slide? (Assume coefficient of static friction $$\mu_s.)$$

Accepted Answer

$$	heta = \arctan \mu_s$$

Question 9

A box slides down a ramp of length $$d$$ and angle $$	heta$$ with coefficient of kinetic friction $$\mu_k. $$Starting from rest, what is its speed at the bottom?

Accepted Answer

$$v = \sqrt{2 g d (\sin 	heta - \mu_k \cos 	heta)}$$

Question 10

Which of the following best describes the force of kinetic friction?

Accepted Answer

$$f_k = \mu_k N$$, where $$N is $$the normal force

Question 11

For a small object moving slowly through water, the fluid friction force is best described by:

Accepted Answer

$$F_{	ext{friction}} = k v$$

Question 12

A falling object reaches terminal velocity when:

Accepted Answer

$$mg = kv$$

Question 13

Which of the following is true about static and kinetic friction?

Accepted Answer

Static friction can be greater than kinetic friction.

Question 14

A $$10.0\ \mathrm{kg}$$ ball of lead falls through air. If the drag force is $$F_{	ext{drag}} = kv^2$ and mg$$ = $$kv^2 at $$terminal velocity, what is the terminal velocity?

Accepted Answer

$$v_t = \sqrt{mg / k}$$

Question 15

A person stands on a scale in an elevator moving downward at constant velocity. What does the scale read?

Accepted Answer

$$mg$$

Question 16

Which of the following is NOT a type of friction discussed in the materials?

Accepted Answer

Magnetic friction

Question 17

In a two-object system connected by a string over a pulley, what is true about the tension in the string?

Accepted Answer

The tension is the same magnitude for both objects but may have different directions.

Question 18

Which of the following best describes what a bathroom scale measures?

Accepted Answer

The normal force exerted by you on the scale

Question 19

A box of mass $$m is $$sliding down a ramp with friction. Which equation gives the net force on the box?

Accepted Answer

$$F_{	ext{net}} = m g \sin 	heta - \mu_k m g \cos 	heta$$

Applying Newton's Laws: Equilibrium, Dynamics, Apparent Weight, and Friction

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