Q: A car of mass $$1500\ \mathrm{kg} is $$moving up a $$10^\circ$$ slope and comes to a stop due to kinetic friction. If the coefficient of kinetic friction is $$\mu_k = 0.80$$, what is the magnitude of the friction force?

$$F_k = \mu_k m g \cos \theta$$

Q: A tightrope walker of mass $$60\ \mathrm{kg}$$ stands at the center of a rope that makes a $$10^\circ$$ angle with the horizontal on each side. What is the tension in the rope?

$$T = \dfrac{mg}{2 \sin \theta}$$

Q: A $$20\ \mathrm{kg}$$ object is at rest at the origin. A force $$F(t)$$ acts on it for $$t = 0 to$$ $$t = 6.0\ \mathrm{s}$$, where $$F(t) is $$piecewise constant: $$F = 2.0\ \mathrm{N}$$ for $$0 \u003c t \u003c 3.0\ \mathrm{s}$$, $$F = 4.0\ \mathrm{N}$$ for $$3.0 \u003c t \u003c 6.0\ \mathrm{s}. $$What is the velocity at $$t = 6.0\ \mathrm{s}$$?

$$v = \dfrac{2.0}{20} \times 3.0 + \dfrac{4.0}{20} \times 3.0$$

Question 1

A 16 kg car and a 2.0 kg car are released from rest on a frictionless inclined plane at the same angle. Which statement best describes their acceleration after being released?

Accepted Answer

Both cars accelerate at the same rate.

Question 2

A small car is pushing a large truck and they are speeding up. Is the force of the car on the truck larger than, smaller than, or equal to the force of the truck on the car?

Accepted Answer

The forces are equal in magnitude.

Question 3

An object of mass $$m is $$hanging from the ceiling of an elevator. The elevator is moving upward and slowing down. The tension in the string is:

Accepted Answer

Less than $$mg$$

Question 4

Given the force vs. acceleration graphs below, which graph represents the largest mass? (Assume all axes are labeled identically.)

Accepted Answer

The graph with the smallest slope.

Question 5

Jacob pulls to the west with a force of 100 N, and Brandon pulls to the north with a force of 90 N on a sled. What is the magnitude of the resultant force?

Accepted Answer

$$\sqrt{100^2$ + 90^2$}$$

Question 6

A car of mass $$1500\ \mathrm{kg} is $$moving up a $$10^\circ$$ slope and comes to a stop due to kinetic friction. If the coefficient of kinetic friction is $$\mu_k = 0.80$$, what is the magnitude of the friction force?

Accepted Answer

$$F_k = \mu_k m g \cos 	heta$$

Question 7

A tightrope walker of mass $$60\ \mathrm{kg}$$ stands at the center of a rope that makes a $$10^\circ$$ angle with the horizontal on each side. What is the tension in the rope?

Accepted Answer

$$T = \dfrac{mg}{2 \sin 	heta}$$

Question 8

A car accelerates from rest to $$160\ \mathrm{m/s} in$$ $$3.8\ \mathrm{s}$$ over a distance of $$300\ \mathrm{m}. $$What is the average acceleration?

Accepted Answer

$$a = \dfrac{2 \Delta x}{t^2$}$$

Question 9

A $$20\ \mathrm{kg}$$ object is at rest at the origin. A force $$F(t)$$ acts on it for $$t = 0 to$$ $$t = 6.0\ \mathrm{s}$$, where $$F(t) is $$piecewise constant: $$F = 2.0\ \mathrm{N}$$ for $$0 \u003c t \u003c 3.0\ \mathrm{s}$$, $$F = 4.0\ \mathrm{N}$$ for $$3.0 \u003c t \u003c 6.0\ \mathrm{s}. $$What is the velocity at $$t = 6.0\ \mathrm{s}$$?

Accepted Answer

$$v = \dfrac{2.0}{20} 	imes 3.0 + \dfrac{4.0}{20} 	imes 3.0$$

Question 10

A person stands on a scale in an elevator. The scale reads $$75\% of $$the person's true weight. What is the acceleration of the elevator?

Accepted Answer

$$a = (1 - 0.75)g$$

Question 11

In a system of pulleys, which configuration provides the greatest mechanical advantage for lifting a mass $$m$$?

Accepted Answer

The system with the most supporting rope segments.

Question 12

A car skids to a halt on a slope. Which force diagram correctly represents the forces acting on the car during the skid?

Accepted Answer

Weight down, normal force perpendicular to slope, friction up the slope.

Question 13

A $$60\ \mathrm{kg}$$ gymnast hangs motionless from a rope. What is the tension in the rope?

Accepted Answer

$$T = mg$$

Question 14

A car of mass $$m$$ accelerates up a frictionless $$	heta-$$degree incline. What is the net force acting on the car?

Accepted Answer

$$F_{net} = m g \sin 	heta$$

Question 15

A block is pulled at constant velocity across a horizontal surface. What is the relationship between the applied force and the friction force?

Accepted Answer

Applied force equals friction force.

Question 16

A $$20\ \mathrm{kg}$$ box is pulled by a rope at an angle of $$30^\circ$$ above the horizontal. If the tension in the rope is $$100\ \mathrm{N}$$, what is the horizontal component of the tension?

Accepted Answer

$$T_x = 100 \cos 30^\circ$$

Question 17

A car of mass $$m is $$moving at velocity $$v$$ and comes to a stop due to friction. What is the stopping distance if the coefficient of kinetic friction is $$\mu_k$$?

Accepted Answer

$$d = \dfrac{v^2$}{2 \mu_k g}$$

Question 18

A $$10\ \mathrm{kg}$$ mass is suspended by two ropes, each making a $$45^\circ$$ angle with the ceiling. What is the tension in each rope?

Accepted Answer

$$T = \dfrac{mg}{2 \sin 45^\circ}$$

Question 19

A $$5\ \mathrm{kg}$$ block is pulled by a force of $$20\ \mathrm{N} on a $$frictionless surface. What is its acceleration?

Accepted Answer

$$a = \dfrac{F}{m}$$

Forces, Motion, and Systems: Study Notes for College Physics

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