Q: A hockey puck slides off the edge of a table at point A with an initial speed of 15.0 m/s and experiences no air resistance. The height of the table above the ground is 1.20 m. What is the time the puck remains in the air before striking the ground?

$$ t = \sqrt{\frac{2h}{g}} = \sqrt{\frac{2 \times 1.20}{9.8}} \approx 0.495 \text{ s} $$

Q: A block of mass 3.0 kg can move without friction on a horizontal table. This block is attached to another block of mass 2.0 kg by a cord that passes over a frictionless pulley. If the masses of the cord and the pulley are negligible, what is the magnitude of the acceleration of the descending block?

$$ a = \frac{m_2$ g}{m_1$ + m_2$} = \frac{2.0 \times 9.8}{3.0 + 2.0} = 3.92 \text{ m/s}^2 $$

Q: A 60.0-kg person rides in an elevator while standing on a scale. The scale reads 480 N. What is the acceleration of the elevator?

$$ a = \frac{N}{m} - g = \frac{480}{60.0} - 9.8 = -1.8 \text{ m/s}^2 $$

Q: A 2.0-kg block slides down a 30\degree incline on a smooth surface with an acceleration of 2 m/s$$^2. $$What is the net force acting on the block?

$$ F_{net} = m a = 2.0 \times 2 = 4.0 \text{ N} $$

Q: A traffic light weighing 100 N is supported by two ropes as shown in the figure. What are the tensions in the ropes if both ropes make equal angles with the horizontal?

$$ T = \frac{W}{2 \cos \theta} $$

Q: A box of mass 6.0 kg is pushed a distance of 2.0 m across a rough warehouse floor by an applied force of 24 N directed at an angle of 30.0\degree below the horizontal. The coefficient of static and kinetic friction between the floor and the box are 0.3 and 0.1, respectively. What is the minimum force needed to set the block in motion?

$$ F_{min} = \mu_s N = \mu_s (mg - F \sin \theta) $$

Q: A helicopter holding a 70-kg package suspended from a rope 5.0 meters long accelerates upward at a rate of 5.3 m/s$$^2. $$Neglect air resistance on the package. What is the tension in the rope?

$$ T = m(g + a) = 70 \times (9.8 + 5.3) = 1,274 \text{ N} $$

Q: Two forces act on a 55-kg object. One force has magnitude 65 N directed 59\degree South of East, and the other has a magnitude 35 N at 32\degree East of North. What is the magnitude of this object's acceleration?

$$ a = \frac{\sqrt{F_1$^2 + F_2$^2 + 2 F_1$ F_2$ \cos \theta}}{m} $$

Q: A block lies on a horizontal frictionless surface. A horizontal force of 100 N is applied to the block giving rise to an acceleration of 2.0 m/s$$^2. $$What is the mass of the block?

$$ m = \frac{F}{a} = \frac{100}{2.0} = 50 \text{ kg} $$

Question 1

A hockey puck slides off the edge of a table at point A with an initial speed of 15.0 m/s and experiences no air resistance. The height of the table above the ground is 1.20 m. What is the time the puck remains in the air before striking the ground?

Accepted Answer

$$ t = \sqrt{\frac{2h}{g}} = \sqrt{\frac{2 	imes 1.20}{9.8}} \approx 0.495 	ext{ s} $$

Question 2

A child throws a ball with an initial speed of 8.00 m/s at an angle of 40.0\degree above the horizontal. The ball leaves her hand 1.00 m above the ground and experiences negligible air resistance. What is the maximum height above the ground that the ball reaches?

Accepted Answer

$$ h_{max} = h_0$ + \frac{(v_0$ \sin \$$theta)^2$$}{2g} = 1.00 + \frac{(8.00 \sin 40.0^\$$circ)^2$$}{2 	imes 9.8} \approx 3.06 	ext{ m} $$

Question 3

A block of mass 3.0 kg can move without friction on a horizontal table. This block is attached to another block of mass 2.0 kg by a cord that passes over a frictionless pulley. If the masses of the cord and the pulley are negligible, what is the magnitude of the acceleration of the descending block?

Accepted Answer

$$ a = \frac{m_2$ g}{m_1$ + m_2$} = \frac{2.0 	imes 9.8}{3.0 + 2.0} = 3.92 	ext{ m/s}^2 $$

Question 4

A 60.0-kg person rides in an elevator while standing on a scale. The scale reads 480 N. What is the acceleration of the elevator?

Accepted Answer

$$ a = \frac{N}{m} - g = \frac{480}{60.0} - 9.8 = -1.8 	ext{ m/s}^2 $$

Question 5

A 2.0-kg block slides down a 30\degree incline on a smooth surface with an acceleration of 2 m/s$$^2. $$What is the net force acting on the block?

Accepted Answer

$$ F_{net} = m a = 2.0 	imes 2 = 4.0 	ext{ N} $$

Question 6

A traffic light weighing 100 N is supported by two ropes as shown in the figure. What are the tensions in the ropes if both ropes make equal angles with the horizontal?

Accepted Answer

$$ T = \frac{W}{2 \cos 	heta} $$

Question 7

A box of mass 6.0 kg is pushed a distance of 2.0 m across a rough warehouse floor by an applied force of 24 N directed at an angle of 30.0\degree below the horizontal. The coefficient of static and kinetic friction between the floor and the box are 0.3 and 0.1, respectively. What is the minimum force needed to set the block in motion?

Accepted Answer

$$ F_{min} = \mu_s N = \mu_s (mg - F \sin 	heta) $$

Question 8

A helicopter holding a 70-kg package suspended from a rope 5.0 meters long accelerates upward at a rate of 5.3 m/s$$^2. $$Neglect air resistance on the package. What is the tension in the rope?

Accepted Answer

$$ T = m(g + a) = 70 	imes (9.8 + 5.3) = 1,274 	ext{ N} $$

Question 9

Two forces act on a 55-kg object. One force has magnitude 65 N directed 59\degree South of East, and the other has a magnitude 35 N at 32\degree East of North. What is the magnitude of this object's acceleration?

Accepted Answer

$$ a = \frac{\sqrt{F_1$^2 + F_2$^2 + 2 F_1$ F_2$ \cos 	heta}}{m} $$

Question 10

A brick is resting on a rough incline as shown in the figure. The friction force acting on the brick, along the incline, is:

Accepted Answer

$$ F_f \leq \mu_s F_N $$

Question 11

A block lies on a horizontal frictionless surface. A horizontal force of 100 N is applied to the block giving rise to an acceleration of 2.0 m/s$$^2. $$What is the mass of the block?

Accepted Answer

$$ m = \frac{F}{a} = \frac{100}{2.0} = 50 	ext{ kg} $$

Question 12

A projectile is fired from point P at the edge of a cliff, with initial velocity components of $$v_{0x}=60.0 m/s $$and $$v_{0y}=17.0 m/s. $$The time of flight of the projectile is 4.0 s. What is the height of the cliff?

Accepted Answer

$$ h = v_{0y} t + \frac{1}{2} a t^2$ = 17.0 	imes 4.0 + \frac{1}{2} (-9.8) 	imes (4.0)^2$ = 68.0 - 78.4 = -10.4 	ext{ m} $$

Question 13

Three boxes A, B, and C are placed on a frictionless surface as shown in the diagram. If you push on box A with a force of 2.85 N, $$m_A = 7.45 kg$$, $$m_B = 4.40 kg$$, and $$m_C = 5.30 kg. $$What is the acceleration of the boxes?

Accepted Answer

$$ a = \frac{F}{m_A + m_B + m_C} = \frac{2.85}{7.45 + 4.40 + 5.30} = 0.155 	ext{ m/s}^2 $$

Question 14

A skier of mass 50 kg starting from rest travels 200 m down a hill that has a 20\degree slope and a uniform surface. When the skier reaches the bottom of the hill, her speed is 30.0 m/s. What is the magnitude of the frictional force if the skier travels directly down the hill?

Accepted Answer

$$ f = mg \sin 	heta - m \frac{v^2$}{2d} $$

Question 15

A student standing on a scale in an elevator notices that the scale reads 645 N. From this information, the student infers that the elevator must be accelerating. What is the direction of acceleration?

Accepted Answer

Upward

Question 16

A box of mass 6.0 kg is at rest on a smooth horizontal floor. A force of 100 N is applied at 37.0\degree above the horizontal. What is the normal force exerted by the floor on the box?

Accepted Answer

$$ N = mg - F \sin 	heta = 6.0 	imes 9.8 - 100 	imes \sin 37.0^\circ = 58.8 - 60.2 = -1.4 	ext{ N} $$

Question 17

A block of mass $$m$$ slides down a rough incline of angle $$	heta$$ with acceleration $$a. $$The coefficient of kinetic friction is $$\mu_k. $$Which equation correctly relates these quantities?

Accepted Answer

$$ a = g (\sin 	heta - \mu_k \cos 	heta) $$

Question 18

A 0.60-kg box is pushed a distance of 2.0 m across a rough warehouse floor by an applied force of 24 N directed at an angle of 30.0\degree below the horizontal. The coefficient of kinetic friction between the floor and the box is 0.1. What is the acceleration of the box while it moves over the rough part of the floor?

Accepted Answer

$$ a = \frac{F \cos 	heta - f_k}{m} $$

Kinematics and Newton's Laws: Study Guide and Problem Review

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