Q: A 5 kg box is pulled across a horizontal surface with a constant velocity by a force of 20 N applied at an angle of $$30^\ ext{o}$$ above the horizontal. What is the coefficient of kinetic friction between the box and the surface?

$$\mu_k = \frac{20 \cos 30^\ ext{o}}{5 \times 9.8 - 20 \sin 30^\ ext{o}}$$

Q: A car of mass 1200 kg rounds a banked curve of radius 50 m at a speed of 20 m/s. The curve is banked at an angle $$\theta$$ such that no friction is required. What is the value of $$\theta$$?

$$\theta = \arctan\left(\frac{v^2$}{rg}\right)$$

Q: A dog (20 kg), a man (80 kg), and a boat (100 kg) are sitting at positions $$x_1 = 0$ m, x_2$ = 2 m$$, and $$x_3 = 4$ m respectively. What is the center of mass of the system?

$$x_{CM} = \frac{20 \times 0 + 80 \times 2 + 100 \times 4}{20 + 80 + 100}$$

Q: A 2 kg block is pulled by a rope with a force of 10 N at an angle of $$45^\ ext{o}$$ above the horizontal. If the coefficient of kinetic friction is 0.2, what is the acceleration of the block?

$$a = \frac{10 \cos 45^\ ext{o} - 0.2 \times (2 \times 9.8 - 10 \sin 45^\ ext{o})}{2}$$

Question 1

A 5 kg box is pulled across a horizontal surface with a constant velocity by a force of 20 N applied at an angle of $$30^\	ext{o}$$ above the horizontal. What is the coefficient of kinetic friction between the box and the surface?

Accepted Answer

$$\mu_k = \frac{20 \cos 30^\	ext{o}}{5 	imes 9.8 - 20 \sin 30^\	ext{o}}$$

Question 2

A car of mass 1200 kg rounds a banked curve of radius 50 m at a speed of 20 m/s. The curve is banked at an angle $$	heta$$ such that no friction is required. What is the value of $$	heta$$?

Accepted Answer

$$	heta = \arctan\left(\frac{v^2$}{rg}ight)$$

Question 3

A 2 kg object is attached to a string and whirled in a horizontal circle of radius 0.5 m at a constant speed of 4 m/s. What is the tension in the string?

Accepted Answer

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

Question 4

Which of the following best describes the Coriolis effect?

Accepted Answer

It is an apparent force observed in rotating reference frames, causing moving objects to deflect.

Question 5

A 70 kg person stands on a scale in an elevator accelerating upward at $$2 	ext{ m/s}^2. $$What is the apparent weight?

Accepted Answer

$$N = m(g + a)$$

Question 6

A block slides down a frictionless inclined plane making an angle $$	heta$$ with the horizontal. What is the acceleration of the block?

Accepted Answer

$$a = g \sin 	heta$$

Question 7

Which statement about inertial and non-inertial frames of reference is correct?

Accepted Answer

Non-inertial frames require fictitious forces to explain motion.

Question 8

A train of mass 10,000 kg is pulled by a locomotive with a force of 40,000 N. If the friction force is 5,000 N, what is the acceleration of the train?

Accepted Answer

$$a = \frac{40,000 - 5,000}{10,000}$$

Question 9

A 3 kg object moves in a circle of radius 2 m with a constant angular velocity $$\omega = 5 	ext{ rad/s}. $$What is the centripetal acceleration?

Accepted Answer

$$a_c = \$$omega^2$$ r$$

Question 10

A dog (20 kg), a man (80 kg), and a boat (100 kg) are sitting at positions $$x_1 = 0$ m, x_2$ = 2 m$$, and $$x_3 = 4$ m respectively. What is the center of mass of the system?

Accepted Answer

$$x_{CM} = \frac{20 	imes 0 + 80 	imes 2 + 100 	imes 4}{20 + 80 + 100}$$

Question 11

A block of 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 if the speed is $$v$$?

Accepted Answer

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

Question 12

A 10 kg box is at rest on a horizontal surface. What is the normal force acting on the box?

Accepted Answer

$$N = 10 	imes 9.8$$

Question 13

A car travels around a flat curve of radius 100 m at a speed of 25 m/s. What is the minimum coefficient of friction required to prevent skidding?

Accepted Answer

$$\mu = \frac{v^2$}{rg}$$

Question 14

Which of the following is NOT a property of Newton’s Second Law?

Accepted Answer

It applies only to objects at rest.

Question 15

A 2 kg block is pulled by a rope with a force of 10 N at an angle of $$45^\	ext{o}$$ above the horizontal. If the coefficient of kinetic friction is 0.2, what is the acceleration of the block?

Accepted Answer

$$a = \frac{10 \cos 45^\	ext{o} - 0.2 	imes (2 	imes 9.8 - 10 \sin 45^\	ext{o})}{2}$$

Question 16

Which of the following statements about centrifugal force is correct?

Accepted Answer

It is an apparent force observed in non-inertial reference frames.

Question 17

A block of mass $$m is $$placed on an inclined plane of angle $$	heta$$ with coefficient of static friction $$\mu_s. $$What is the minimum value of $$\mu_s to $$prevent the block from sliding?

Accepted Answer

$$\mu_s = 	an 	heta$$

Question 18

A 1 kg object moves in a circle of radius 2 m with a speed of 3 m/s. What is the net force acting on the object?

Accepted Answer

$$F = \frac{mv^2$}{r}$$

Question 19

Which of the following is the correct relationship between angular and linear velocity?

Accepted Answer

$$v = \omega r$$

Physics with Calculus: Dynamics and Circular Motion Study Guidance

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