Q: A 2.0 kg object slides down a frictionless incline that is 85 cm long. If the angle of the incline is $$30^\ ext{o}$$, what is the net force acting on the object parallel to the incline?

$$F = 2.0 \\text{ kg} \\times 9.8 \\text{ m/s}^2 \\times \\sin(30^\ ext{o}) = 9.8 \\text{ N}$$

Q: A box of mass 5 kg is pulled to the right with a force of 20 N on a rough surface. If the frictional force is 8 N, what is the net force acting on the box?

$$F_{\\text{net}} = 20 \\text{ N} - 8 \\text{ N} = 12 \\text{ N}$$

Q: A car of mass 1200 kg accelerates from rest to 20 m/s in 10 seconds. What is the net force acting on the car?

$$F = m a = 1200 \\text{ kg} \\times \\frac{20 \\text{ m/s}}{10 \\text{ s}} = 2400 \\text{ N}$$

Q: A 3 kg block is at rest on a horizontal surface. If the coefficient of friction is $$0.4$$, what is the maximum static friction force that can act on the block?

$$F_{\\text{max}} = \\mu_s m g = 0.4 \\times 3 \\text{ kg} \\times 9.8 \\text{ m/s}^2 = 11.76 \\text{ N}$$

Q: A 10 kg object is dropped from a height and reaches a velocity of 6.8 m/s just before hitting the ground. What is the magnitude of the net force acting on the object during its fall, assuming only gravity acts?

$$F = m g = 10 \\text{ kg} \\times 9.8 \\text{ m/s}^2 = 98 \\text{ N}$$

Q: A student pushes a 4 kg box across a floor with a constant velocity. If the frictional force is 10 N, what is the magnitude of the applied force?

$$F_{\\text{applied}} = F_{\\text{friction}} = 10 \\text{ N}$$

Q: A 2 kg block slides down a ramp with an acceleration of $$6.8 \\text{ m/s}^2. $$What is the net force acting on the block?

$$F = m a = 2 \\text{ kg} \\times 6.8 \\text{ m/s}^2 = 13.6 \\text{ N}$$

Q: A block is pulled up a 30$$^\text{o}$$ incline with a force parallel to the incline. If the block has a mass of 5 kg and the acceleration is $$2 \\text{ m/s}^2$$, what is the total force required to move the block up the incline (ignore friction)?

$$F = m a + m g \\sin(30^\ ext{o}) = 5 \\text{ kg} \\times 2 \\text{ m/s}^2 + 5 \\text{ kg} \\times 9.8 \\text{ m/s}^2 \\times 0.5 = 10 + 24.5 = 34.5 \\text{ N}$$

Q: A 7 kg object is pulled horizontally with a force of 30 N. If the object accelerates at $$2 \\text{ m/s}^2$$, what is the frictional force acting on the object?

$$F_{\\text{friction}} = F_{\\text{applied}} - m a = 30 \\text{ N} - 7 \\text{ kg} \\times 2 \\text{ m/s}^2 = 30 - 14 = 16 \\text{ N}$$

Question 1

A 2.0 kg object slides down a frictionless incline that is 85 cm long. If the angle of the incline is $$30^\	ext{o}$$, what is the net force acting on the object parallel to the incline?

Accepted Answer

$$F = 2.0 \text{ kg} \times 9.8 \text{ m/s}^2 \times \sin(30^\	ext{o}) = 9.8 \text{ N}$$

Question 2

A box of mass 5 kg is pulled to the right with a force of 20 N on a rough surface. If the frictional force is 8 N, what is the net force acting on the box?

Accepted Answer

$$F_{\text{net}} = 20 \text{ N} - 8 \text{ N} = 12 \text{ N}$$

Question 3

A car of mass 1200 kg accelerates from rest to 20 m/s in 10 seconds. What is the net force acting on the car?

Accepted Answer

$$F = m a = 1200 \text{ kg} \times \frac{20 \text{ m/s}}{10 \text{ s}} = 2400 \text{ N}$$

Question 4

Which of the following best describes Newton's Second Law of Motion?

Accepted Answer

The net force acting on an object is equal to the mass of the object multiplied by its acceleration: $$F = m a$$

Question 5

A 3 kg block is at rest on a horizontal surface. If the coefficient of friction is $$0.4$$, what is the maximum static friction force that can act on the block?

Accepted Answer

$$F_{\text{max}} = \mu_s m g = 0.4 \times 3 \text{ kg} \times 9.8 \text{ m/s}^2 = 11.76 \text{ N}$$

Question 6

A 10 kg object is dropped from a height and reaches a velocity of 6.8 m/s just before hitting the ground. What is the magnitude of the net force acting on the object during its fall, assuming only gravity acts?

Accepted Answer

$$F = m g = 10 \text{ kg} \times 9.8 \text{ m/s}^2 = 98 \text{ N}$$

Question 7

A student pushes a 4 kg box across a floor with a constant velocity. If the frictional force is 10 N, what is the magnitude of the applied force?

Accepted Answer

$$F_{\text{applied}} = F_{\text{friction}} = 10 \text{ N}$$

Question 8

A 2 kg block slides down a ramp with an acceleration of $$6.8 \text{ m/s}^2. $$What is the net force acting on the block?

Accepted Answer

$$F = m a = 2 \text{ kg} \times 6.8 \text{ m/s}^2 = 13.6 \text{ N}$$

Question 9

A block is pulled up a 30$$^	ext{o}$$ incline with a force parallel to the incline. If the block has a mass of 5 kg and the acceleration is $$2 \text{ m/s}^2$$, what is the total force required to move the block up the incline (ignore friction)?

Accepted Answer

$$F = m a + m g \sin(30^\	ext{o}) = 5 \text{ kg} \times 2 \text{ m/s}^2 + 5 \text{ kg} \times 9.8 \text{ m/s}^2 \times 0.5 = 10 + 24.5 = 34.5 \text{ N}$$

Question 10

A 7 kg object is pulled horizontally with a force of 30 N. If the object accelerates at $$2 \text{ m/s}^2$$, what is the frictional force acting on the object?

Accepted Answer

$$F_{\text{friction}} = F_{\text{applied}} - m a = 30 \text{ N} - 7 \text{ kg} \times 2 \text{ m/s}^2 = 30 - 14 = 16 \text{ N}$$

Question 11

A 1.5 kg book is at rest on a table. What is the normal force exerted by the table on the book?

Accepted Answer

$$F_N = m g = 1.5 \text{ kg} \times 9.8 \text{ m/s}^2 = 14.7 \text{ N}$$

Question 12

A 2 kg block is sliding down a ramp with a frictional force of 5 N acting against its motion. If the gravitational force component down the ramp is 9.8 N, what is the net force acting on the block?

Accepted Answer

$$F_{\text{net}} = 9.8 \text{ N} - 5 \text{ N} = 4.8 \text{ N}$$

Question 13

A 6 kg object is pulled with a force of 40 N at an angle of $$30^\	ext{o}$$ above the horizontal. What is the horizontal component of the applied force?

Accepted Answer

$$F_x = 40 \text{ N} \times \cos(30^\	ext{o}) = 40 \times 0.866 = 34.64 \text{ N}$$

Question 14

A 2 kg block is pushed with a force of 15 N on a horizontal surface. If the block accelerates at $$5 \text{ m/s}^2$$, what is the frictional force acting on the block?

Accepted Answer

$$F_{\text{friction}} = F_{\text{applied}} - m a = 15 \text{ N} - 2 \text{ kg} \times 5 \text{ m/s}^2 = 15 - 10 = 5 \text{ N}$$

Question 15

A 5 kg box is at rest on a ramp inclined at $$45^\	ext{o}. $$What is the component of the gravitational force acting parallel to the ramp?

Accepted Answer

$$F_{\text{parallel}} = m g \sin(45^\	ext{o}) = 5 \text{ kg} \times 9.8 \text{ m/s}^2 \times 0.707 = 34.7 \text{ N}$$

Question 16

A 2 kg block is sliding down a ramp with a frictional force of 3 N acting against its motion. If the block's acceleration is $$3 \text{ m/s}^2$$, what is the net force acting on the block?

Accepted Answer

$$F_{\text{net}} = m a = 2 \text{ kg} \times 3 \text{ m/s}^2 = 6 \text{ N}$$

Question 17

A 4 kg block is pulled with a force of 20 N on a horizontal surface. If the block moves with a constant velocity, what is the coefficient of friction between the block and the surface?

Accepted Answer

$$\mu = \frac{F_{\text{friction}}}{m g} = \frac{20}{4 \times 9.8} = \frac{20}{39.2} = 0.51$$

Forces and Motion: Study Notes and Practice Problems

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