Q: A block with mass $$m$$ starts from rest and slides down a plane inclined at angle $$\theta. $$The coefficient of kinetic friction is $$\mu_k. $$Which expression would you use to solve for the block's speed after it has traveled a distance $$L$$ down the plane?

$$mgL\sin\theta - \mu_k mgL\cos\theta = \frac{1}{2}mv^2$

Q: A shower curtain rod consists of two telescoping cylinders connected by an internal spring with $$k = 750\ \mathrm{N/m}$$ and a relaxed length $$L_0 = 2.6$$\ \mathrm{m}$$. If the rod is placed between two walls a distance L = 2.5$$\ \mathrm{m}$$ apart, what is the magnitude of the spring force at each end?

$$F = k(L_0$ - L) = 750 \times (2.6 - 2.5) = 75\ \mathrm{N}$$

Q: A physical therapist is testing the strength of a patient's biceps muscle. The patient holds a ball of mass $$M at a $$distance $$r$$ from the elbow joint, with the arm at an angle of $$105^\circ$$ with respect to the forearm. What is the magnitude of the maximum force the biceps can withstand, $$F_{biceps}$$?

$$F_{biceps} = \frac{Mg(r_{ball})}{r_{biceps} \sin\theta}$$

Q: You want to model what happens when a person falls. You build an apparatus where a light rod has two small equal masses fixed to it. The rod can pivot around its end. If $$m_1 = 1$$\ \mathrm{kg}$$ and m_2$ = 1\ \mathrm{kg}$$, what is the torque caused by gravity about the pivot when $$\theta = 45^\circ$$?

$$\tau = (m_1$ + m_2$)gL \sin\theta$$

Q: A ball of mass $$M$$ and radius $$R is $$held in a patient's hand. The patient extends their arm at an angle of $$105^\circ$$ with respect to the forearm. If the center of mass of the ball is $$15\ \mathrm{cm}$$ from the elbow, and the arm has a mass $$m_{arm} = 2.0\ \mathrm{kg}$$, what is the torque about the elbow joint due to the ball?

$$\tau = Mg \times 0.15 \sin(105^\circ)$$

Question 1

Three books X, Y, and Z rest on a table. The weights are $$4\ \mathrm{N} (X$$), $$5\ \mathrm{N} (Y$$), and $$10\ \mathrm{N} (Z). $$What is the net force acting on book Y?

Accepted Answer

$$9\ \mathrm{N}$$

Question 2

A heavy box is pushed down a ramp by a girl. At the bottom, she stops pushing and the box comes to a stop due to friction. For the entire process, the work done by the girl on the box was ____ and the work done by gravity on the box was ____.

Accepted Answer

zero; positive

Question 3

A mass moves in a circle at constant speed. The acceleration of the mass is:

Accepted Answer

always perpendicular to the velocity

Question 4

You push a heavy box straight up a ramp (with friction). Which of the following quantities will be negative?

Accepted Answer

The work done by gravity on the box

Question 5

A block with mass $$m$$ starts from rest and slides down a plane inclined at angle $$	heta. $$The coefficient of kinetic friction is $$\mu_k. $$Which expression would you use to solve for the block's speed after it has traveled a distance $$L$$ down the plane?

Accepted Answer

$$mgL\sin	heta - \mu_k mgL\cos	heta = \frac{1}{2}mv^2$

Question 6

Two children are standing on a merry-go-round that is at rest. You apply a fixed torque $$	au$$ for a total time $$T$$, and measure the final speed of the merry-go-round. Which of the following scenarios would lead to the fastest final speed of the merry-go-round, keeping $$	au$$ and $$T$$ fixed?

Accepted Answer

The children stand near the center of the merry-go-round

Question 7

A stick has its bottom end attached to a wall by a pivot, and is held up by a massless string attached to its other end. Which scenario has the smallest tension in the string?

Accepted Answer

The string is at a steep angle above the stick

Question 8

A shower curtain rod consists of two telescoping cylinders connected by an internal spring with $$k = 750\ \mathrm{N/m}$$ and a relaxed length $$L_0 = 2.6$$\ \mathrm{m}$$. If the rod is placed between two walls a distance L = 2.5$$\ \mathrm{m}$$ apart, what is the magnitude of the spring force at each end?

Accepted Answer

$$F = k(L_0$ - L) = 750 	imes (2.6 - 2.5) = 75\ \mathrm{N}$$

Question 9

A mass $$m is $$placed on a spring on a horizontal surface with friction. The spring is compressed a distance $$d by $$the mass, then released. It travels to the right, finally coming to rest at $$x = L. $$What is the coefficient of kinetic friction $$\mu_k$$ between the mass and the floor?

Accepted Answer

$$\mu_k = \frac{kd^2$}{2mgL}$$

Question 10

You hold a child ($$m = 20\ \mathrm{kg}) on a $$swing at an angle of $$	heta = 60^\circ$$ from the vertical. The swing is held by cables of length $$l = 5\ \mathrm{m}. If $$you apply force strictly in the horizontal direction, what is the force required to hold the child in place?

Accepted Answer

$$F = mg \sin	heta$$

Question 11

A physical therapist is testing the strength of a patient's biceps muscle. The patient holds a ball of mass $$M at a $$distance $$r$$ from the elbow joint, with the arm at an angle of $$105^\circ$$ with respect to the forearm. What is the magnitude of the maximum force the biceps can withstand, $$F_{biceps}$$?

Accepted Answer

$$F_{biceps} = \frac{Mg(r_{ball})}{r_{biceps} \sin	heta}$$

Question 12

You want to model what happens when a person falls. You build an apparatus where a light rod has two small equal masses fixed to it. The rod can pivot around its end. If $$m_1 = 1$$\ \mathrm{kg}$$ and m_2$ = 1\ \mathrm{kg}$$, what is the torque caused by gravity about the pivot when $$	heta = 45^\circ$$?

Accepted Answer

$$	au = (m_1$ + m_2$)gL \sin	heta$$

Question 13

What is the ratio of the speeds of two masses $$m_1$$ and $$m_2 at $$any point as they fall from the same height?

Accepted Answer

$$\frac{v_1$}{v_2$} = 1$$

Question 14

Standing upright with your arms by your sides, you fall backward. How fast are you moving right before hitting the ground? Assume your body is a uniform rigid rod of length $$L. $$The moment of inertia for a rod rotating about one end is $$I = \frac{1}{3}mL^2$. What is the angular speed $$\omega$$ just before impact?

Accepted Answer

$$\omega = \sqrt{\frac{3g}{L}}$$

Question 15

A ball of mass $$M$$ and radius $$R is $$held in a patient's hand. The patient extends their arm at an angle of $$105^\circ$$ with respect to the forearm. If the center of mass of the ball is $$15\ \mathrm{cm}$$ from the elbow, and the arm has a mass $$m_{arm} = 2.0\ \mathrm{kg}$$, what is the torque about the elbow joint due to the ball?

Accepted Answer

$$	au = Mg 	imes 0.15 \sin(105^\circ)$$

Question 16

A block slides down a frictionless incline of angle $$	heta$$ and length $$L. $$What is its speed at the bottom?

Accepted Answer

$$v = \sqrt{2gL\sin	heta}$$

Question 17

A mass $$m is $$attached to a string and swung in a vertical circle of radius $$r. At $$the lowest point, what is the tension in the string?

Accepted Answer

$$T = mg + \frac{mv^2$}{r}$$

Midterm practice

스터디 가이드 - 연습 문제

학습 가이드 - 플래시카드