Q: A skier of mass $$m$$ slides down a frictionless slope inclined at $$\theta = 27^\circ. $$What is the skier's acceleration?

$$a = g \sin \theta = (9.8\ \mathrm{m/s}^2) \sin 27^\circ = 4.4\ \mathrm{m/s}^2$$

Question 1

A 1500 kg car is being towed at a constant speed by a rope that makes a 20° angle with the horizontal. If the friction force opposing the car's motion is 320 N, what is the tension in the rope?

Accepted Answer

$$T = \frac{320\ \mathrm{N}}{\cos 20^\circ} = 340\ \mathrm{N}$$

Question 2

Which of the following statements about static and dynamic equilibrium is correct?

Accepted Answer

In both static and dynamic equilibrium, the net force acting on the object is zero.

Question 3

A 1.2 kg book is pressed down with a 15 N force while resting on a table. What is the normal force exerted by the table on the book?

Accepted Answer

$$n = F + w = 15\ \mathrm{N} + (1.2\ \mathrm{kg})(9.8\ \mathrm{m/s}^2) = 27\ \mathrm{N}$$

Question 4

A golfer putts a 46 g ball with a speed of 3.0 m/s. If friction exerts a 0.020 N retarding force, how far will the ball travel before stopping?

Accepted Answer

$$x = \frac{-(v_0$)^2$$}{2a} = \frac{-(3.0\ \mathrm{m/s}$$)^2$$}{2 	imes (-0.435\ \mathrm{m/s}^2)} = 10\ \mathrm{m}$

Question 5

A box is sitting on the floor of an elevator that is accelerating upward. Which of the following is true about the normal force $$n on $$the box?

Accepted Answer

$$n \u003e mg$$

Question 6

A skier of mass $$m$$ slides down a frictionless slope inclined at $$	heta = 27^\circ. $$What is the skier's acceleration?

Accepted Answer

$$a = g \sin 	heta = (9.8\ \mathrm{m/s}^2) \sin 27^\circ = 4.4\ \mathrm{m/s}^2$$

Question 7

A 100 N box is at rest. It is pulled by a 30 N horizontal force. The coefficient of static friction is $$\mu_s = 0.4. $$Will the box move?

Accepted Answer

No, because $$30\ \mathrm{N} \u003c f_{s,\max} = \mu_s n = 40\ \mathrm{N}$$

Question 8

Carol pushes a 32 kg sofa across the floor at constant speed using slippery disks. The coefficient of kinetic friction is $$\mu_k = 0.08. $$What force must she apply?

Accepted Answer

$$F = \mu_k m g = (0.08)(32\ \mathrm{kg})(9.8\ \mathrm{m/s}^2) = 25\ \mathrm{N}$$

Question 9

Which of the following best describes the difference between mass and weight?

Accepted Answer

Mass is a measure of an object's inertia; weight is the gravitational force acting on the object.

Question 10

A block of mass $$m is $$pulled by a rope over a massless, frictionless pulley. The other end of the rope is attached to a hanging mass $$M. If$$ $$M \u003e m$$, what is the acceleration of the system?

Accepted Answer

$$a = \frac{(M - m)g}{M + m}$$

Question 11

A 100 kg stagehand and a 200 kg stage set are connected by a massless rope over a frictionless pulley. When the rope is released, what is the acceleration of the stagehand?

Accepted Answer

$$a = \frac{(200\ \mathrm{kg} - 100\ \mathrm{kg})g}{200\ \mathrm{kg} + 100\ \mathrm{kg}} = \frac{100g}{300} = 0.33g \approx 3.3\ \mathrm{m/s}^2$$

Question 12

Which of the following is true about the tension in a massless rope passing over a massless, frictionless pulley?

Accepted Answer

The tension is the same on both sides of the pulley.

Question 13

A block of mass $$m is $$being pulled across a horizontal surface at constant speed. Which of the following is true about the net force on the block?

Accepted Answer

The net force is zero because the block is in dynamic equilibrium.

Question 14

A wheel is rolling without slipping on a surface. Which type of friction is primarily responsible for this motion?

Accepted Answer

Rolling friction

Question 15

Which of the following best describes the direction and magnitude of the drag force $$D on an $$object moving through a fluid at high speed?

Accepted Answer

$$D is $$opposite to the velocity and increases with the square of the speed: $$D = C \rho A v^2$

Question 16

Two blocks, A and B, are in contact and are being pushed to the right on a frictionless surface. Block A has a larger mass than block B. Which statement about the force that A exerts on B and the force that B exerts on A is correct?

Accepted Answer

The forces are equal in magnitude and opposite in direction, according to Newton's third law.

Question 17

A person stands on a scale in an elevator accelerating downward. How does the scale reading (apparent weight) compare to the person's true weight?

Accepted Answer

The apparent weight is less than the true weight.

Question 18

A block is being pulled across a rough surface at constant speed. If the coefficient of kinetic friction is doubled, what happens to the force required to keep the block moving at constant speed?

Accepted Answer

The required force doubles.

Forces and Newton's Laws: Equilibrium, Tension, and Newton's Second Law

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