Q: A 1 kg object is dropped from a height of 10 m. What is its speed just before hitting the ground? (Neglect air resistance, $$g = 9.8 m/s$^2)$$

$$v = \sqrt{2 \times 9.8 \times 10} = 14 m/s$$

Q: A 2 kg mass is attached to a string and swung in a vertical circle of radius 1 m. At the lowest point, its speed is 4 m/s. What is the tension in the string at this point? ($$g = 9.8 m/s$^2)$$

$$T = 2 \times 9.8 + 2 \times 4^2$ / 1 = 19.6 + 32 = 51.6 N$$

Q: A 0.2 kg ball is moving at 5 m/s and collides inelastically with a 0.3 kg ball at rest. What is their final velocity after the collision?

$$v_f = (0.2 \times 5) / 0.5 = 2 m/s$$

Q: A 10 kg box is pulled up a 5 m long ramp inclined at 30$$^\circ to $$the horizontal by a constant force parallel to the ramp. If the box moves at constant speed, what is the work done by the force?

$$W = m g h = 10 \times 9.8 \times 2.5 = 245 J$$

Question 1

A car of mass $$m is $$moving in a circle of radius $$r at a $$constant speed $$v. $$What is the magnitude of the net force acting on the car, and in which direction does it point?

Accepted Answer

$$F = m v^2$ / r$$, directed toward the center of the circle

Question 2

A block of mass $$m$$ slides down a frictionless incline of height $$h. $$What is its speed at the bottom of the incline?

Accepted Answer

$$v = \sqrt{2 g h}$$

Question 3

Which of the following best describes the work done by a constant force $$\vec{F}$$ acting over a displacement $$\vec{\Delta x}$$?

Accepted Answer

$$W = \vec{F} \cdot \vec{\Delta x}$$

Question 4

A 2 kg object is moving at 3 m/s. What is its kinetic energy?

Accepted Answer

$$KE = 6 J$$

Question 5

A ball is thrown vertically upward with an initial speed $$v_0. $$Neglecting air resistance, which of the following statements about its energy at the highest point is correct?

Accepted Answer

Its kinetic energy is zero and its potential energy is maximum.

Question 6

A force $$F is $$applied to a box, moving it a distance $$d at an $$angle $$	heta$$ above the horizontal. What is the work done by the force?

Accepted Answer

$$W = F d \cos 	heta$$

Question 7

Which of the following is a correct statement of the conservation of mechanical energy for a system with no non-conservative forces?

Accepted Answer

$$K_i + U_i = K_f + U_f$$

Question 8

A 0.5 kg ball moving at 4 m/s collides elastically with a stationary 0.5 kg ball. What is the velocity of the first ball after the collision?

Accepted Answer

0 m/s

Question 9

A block of mass $$m is $$attached to a string and swung in a horizontal circle of radius $$r at $$constant speed $$v. $$What is the tension in the string?

Accepted Answer

$$T = m v^2$ / r$$

Question 10

A 3 kg object is moving with a velocity of 2 m/s. What is its momentum?

Accepted Answer

$$p = 6 kg m/s$$

Question 11

A force acts on a 2 kg object, changing its velocity from 1 m/s to 5 m/s over 2 seconds. What is the average force applied?

Accepted Answer

$$F = 4 N$$

Question 12

Which of the following is the correct integral definition of work?

Accepted Answer

$$W = \int \vec{F} \cdot d\vec{x}$$

Question 13

A 1 kg object is dropped from a height of 10 m. What is its speed just before hitting the ground? (Neglect air resistance, $$g = 9.8 m/s$^2)$$

Accepted Answer

$$v = \sqrt{2 	imes 9.8 	imes 10} = 14 m/s$$

Question 14

Which of the following best describes an inelastic collision?

Accepted Answer

Kinetic energy is not conserved, but momentum is conserved.

Question 15

A 5 kg object is moving at 2 m/s. If a constant force of 10 N acts in the direction of motion for 3 seconds, what is the final velocity?

Accepted Answer

$$v_f = 8 m/s$$

Question 16

Which of the following is the correct expression for power in terms of force and velocity?

Accepted Answer

$$P = \vec{F} \cdot \vec{v}$$

Question 17

A 2 kg mass is attached to a string and swung in a vertical circle of radius 1 m. At the lowest point, its speed is 4 m/s. What is the tension in the string at this point? ($$g = 9.8 m/s$^2)$$

Accepted Answer

$$T = 2 	imes 9.8 + 2 	imes 4^2$ / 1 = 19.6 + 32 = 51.6 N$$

Question 18

A 0.2 kg ball is moving at 5 m/s and collides inelastically with a 0.3 kg ball at rest. What is their final velocity after the collision?

Accepted Answer

$$v_f = (0.2 	imes 5) / 0.5 = 2 m/s$$

Question 19

A 10 kg box is pulled up a 5 m long ramp inclined at 30$$^\circ to $$the horizontal by a constant force parallel to the ramp. If the box moves at constant speed, what is the work done by the force?

Accepted Answer

$$W = m g h = 10 	imes 9.8 	imes 2.5 = 245 J$$

PHYS407 Exam 3 Study Guide: Dynamics, Conservation Laws, and Problem Solving

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