Q: A 2 kg object is acted upon by a net force of 10 N. What is its acceleration?

$$a = \frac{10}{2} = 5\ \text{m/s}^2$$

Q: A person stands on a scale in an elevator accelerating upward at $$2\ \text{m/s}^2. If $$the person's mass is $$70\ \text{kg}$$, what is the apparent weight?

$$W_{\text{apparent}} = 70 \times (9.8 + 2) = 826\ \text{N}$$

Q: A 5 kg object is suspended from a rope. If the object is accelerating downward at $$3\ \text{m/s}^2$$, what is the tension in the rope?

$$T = 5 \times (9.8 - 3) = 34\ \text{N}$$

Q: A 1,000 kg car rounds a flat curve of radius $$50\ \text{m} at a $$speed of $$20\ \text{m/s}. $$What is the minimum friction force required to keep the car from skidding?

$$F = \frac{m v^2$}{r} = \frac{1000 \times 20^2$}{50} = 8,000\ \text{N}$$

Q: What is the gravitational force between the Earth ($$M = 5.97 \times 10$$^{24}$$\ \text{kg}) $$and a 70 kg person standing on its surface ($$r = 6.37 \times 10^6$\ \text{m}$$)?

$$F = \frac{G M m}{r^2$} = \frac{6.67 \times 10$$^{-11}$$ \times 5.97 \times 10$$^{24}$$ \times 70}{(6.37 \times 10^6$)^2$$} \approx 686\ \text{N}$

Q: A 2 kg block is pushed 5 m across a horizontal surface with a constant force of 10 N. How much work is done by the force?

$$W = F \cdot d = 10 \times 5 = 50\ \text{J}$$

Q: A spring with spring constant $$k = 200\ \text{N/m} is $$compressed by $$0.1\ \text{m}. $$What is the potential energy stored in the spring?

$$U = \frac{1}{2} k x^2$ = \frac{1}{2} \times 200 \times (0.1)^2$ = 1\ \text{J}$$

Q: A 3 kg object falls from a height of 10 m. Ignoring air resistance, what is its speed just before hitting the ground?

$$v = \sqrt{2 g h} = \sqrt{2 \times 9.8 \times 10} \approx 14\ \text{m/s}$$

Q: A 1 kg object is moving at $$5\ \text{m/s}. $$What is its kinetic energy?

$$KE = \frac{1}{2} m v^2$ = \frac{1}{2} \times 1 \times 25 = 12.5\ \text{J}$$

Question 1

A car of mass $$m is $$traveling at constant velocity on a straight, level road. According to Newton's 1st Law, which statement best describes the net force acting on the car?

Accepted Answer

The net force is zero because the car's velocity is constant.

Question 2

A 2 kg object is acted upon by a net force of 10 N. What is its acceleration?

Accepted Answer

$$a = \frac{10}{2} = 5\ 	ext{m/s}^2$$

Question 3

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

Accepted Answer

$$W_{	ext{apparent}} = 70 	imes (9.8 + 2) = 826\ 	ext{N}$$

Question 4

A 5 kg object is suspended from a rope. If the object is accelerating downward at $$3\ 	ext{m/s}^2$$, what is the tension in the rope?

Accepted Answer

$$T = 5 	imes (9.8 - 3) = 34\ 	ext{N}$$

Question 5

A 1,000 kg car rounds a flat curve of radius $$50\ 	ext{m} at a $$speed of $$20\ 	ext{m/s}. $$What is the minimum friction force required to keep the car from skidding?

Accepted Answer

$$F = \frac{m v^2$}{r} = \frac{1000 	imes 20^2$}{50} = 8,000\ 	ext{N}$$

Question 6

What is the gravitational force between the Earth ($$M = 5.97 	imes 10$$^{24}$$\ 	ext{kg}) $$and a 70 kg person standing on its surface ($$r = 6.37 	imes 10^6$\ 	ext{m}$$)?

Accepted Answer

$$F = \frac{G M m}{r^2$} = \frac{6.67 	imes 10$$^{-11}$$ 	imes 5.97 	imes 10$$^{24}$$ 	imes 70}{(6.37 	imes 10^6$)^2$$} \approx 686\ 	ext{N}$

Question 7

A satellite orbits Earth in a circular orbit of radius $$r. $$What is the speed required to maintain this orbit?

Accepted Answer

$$v = \sqrt{\frac{G M}{r}}$$

Question 8

A 2 kg block is pushed 5 m across a horizontal surface with a constant force of 10 N. How much work is done by the force?

Accepted Answer

$$W = F \cdot d = 10 	imes 5 = 50\ 	ext{J}$$

Question 9

A spring with spring constant $$k = 200\ 	ext{N/m} is $$compressed by $$0.1\ 	ext{m}. $$What is the potential energy stored in the spring?

Accepted Answer

$$U = \frac{1}{2} k x^2$ = \frac{1}{2} 	imes 200 	imes (0.1)^2$ = 1\ 	ext{J}$$

Question 10

A 3 kg object falls from a height of 10 m. Ignoring air resistance, what is its speed just before hitting the ground?

Accepted Answer

$$v = \sqrt{2 g h} = \sqrt{2 	imes 9.8 	imes 10} \approx 14\ 	ext{m/s}$$

Question 11

A 1 kg object is moving at $$5\ 	ext{m/s}. $$What is its kinetic energy?

Accepted Answer

$$KE = \frac{1}{2} m v^2$ = \frac{1}{2} 	imes 1 	imes 25 = 12.5\ 	ext{J}$$

Question 12

A 2 kg object is initially at rest. A constant force acts on it for 4 seconds, giving it a final velocity of $$8\ 	ext{m/s}. $$What is the impulse delivered to the object?

Accepted Answer

$$J = \Delta p = m \Delta v = 2 	imes 8 = 16\ 	ext{kg} \cdot 	ext{m/s}$$

Question 13

Two objects, one of mass $$3\ 	ext{kg}$$ moving at $$4\ 	ext{m/s}$$ and another of mass $$2\ 	ext{kg} at $$rest, collide and stick together. What is their final velocity?

Accepted Answer

$$v_f = \frac{3 	imes 4 + 2 	imes 0}{3 + 2} = \frac{12}{5} = 2.4\ 	ext{m/s}$$

Question 14

A 1 kg ball moving at $$6\ 	ext{m/s}$$ collides elastically with a stationary 1 kg ball. What is the velocity of the first ball after the collision?

Accepted Answer

$$v_1$$' = 0\ 	ext{m/s}$$

Question 15

A uniform rod of length $$2\ 	ext{m}$$ and mass $$4\ 	ext{kg}$$ has two masses attached: $$1\ 	ext{kg} at $$one end and $$3\ 	ext{kg} at $$the other. Where is the center of mass measured from the $$1\ 	ext{kg}$$ end?

Accepted Answer

$$x_{	ext{cm}} = \frac{1 	imes 0 + 3 	imes 2}{1 + 3} = \frac{6}{4} = 1.5\ 	ext{m}$$

Question 16

A disk of radius $$0.5\ 	ext{m}$$ rotates from rest with a constant angular acceleration of $$4\ 	ext{rad/s}^2. $$What is its angular velocity after $$3\ 	ext{s}$$?

Accepted Answer

$$\omega = \alpha t = 4 	imes 3 = 12\ 	ext{rad/s}$$

Question 17

A force of $$20\ 	ext{N} is $$applied tangentially to the rim of a wheel of radius $$0.4\ 	ext{m}. $$What is the torque produced?

Accepted Answer

$$	au = F r = 20 	imes 0.4 = 8\ 	ext{N} \cdot 	ext{m}$$

Question 18

A beam is supported at both ends and has a weight of $$100\ 	ext{N}$$ hanging $$2\ 	ext{m}$$ from the left end of a $$5\ 	ext{m}$$ beam. What is the upward force at the right support for equilibrium?

Accepted Answer

$$F_{	ext{right}} = \frac{2}{5} 	imes 100 = 40\ 	ext{N}$$

Question 19

A steel wire of length $$1\ 	ext{m}$$ and cross-sectional area $$1 	imes 10$$^{-6}$$\ 	ext{m}^2 is $$stretched by a force of $$100\ 	ext{N}. If $$Young's modulus for steel is $$2 	imes 10$$^{11}$$\ 	ext{N/m}^2$$, what is the elongation?

Accepted Answer

$$\Delta L = \frac{F L}{A Y} = \frac{100 	imes 1}{1 	imes 10$$^{-6}$$ 	imes 2 	imes 10$$^{11}$$} = 5 	imes 10$$^{-4}$$\ 	ext{m}$$

EXAM 2 PT 2

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