Q: Which of the following correctly matches the SI prefix with its corresponding power of ten?

micro- corresponds to $$\times 10$$^{-6}$$

Q: A 5 kg mass is dropped from a height of 10 m. Ignoring air resistance, what is its velocity just before hitting the ground? (Use $$g = 9.8\, \text{m/s}^2)$$

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

Q: A 3 kg object moving at $$4\, \text{m/s}$$ collides with a stationary 2 kg object. If they stick together, what is their final velocity?

$$v_f = \frac{3 \times 4}{3 + 2} = 2.4\, \text{m/s}$$

Q: A 1 kg ball is thrown vertically upward with an initial velocity of $$10\, \text{m/s}. $$What is its maximum height? (Use $$g = 9.8\, \text{m/s}^2)$$

$$h = \frac{v_0$^2}{2g} = \frac{100}{19.6} \approx 5.1\, \text{m}$$

Q: A 0.5 kg ball moving at $$2\, \text{m/s}$$ bounces off a wall and returns at $$-1\, \text{m/s}. $$What is the change in momentum?

$$\Delta p = m (v_f - v_i) = 0.5 \times (-1 - 2) = -1.5\, \text{kg m/s}$$

Question 1

Which of the following correctly matches the SI prefix with its corresponding power of ten?

Accepted Answer

micro- corresponds to $$	imes 10$$^{-6}$$

Question 2

A car accelerates from rest at a constant rate. Which kinematic equation would you use to find the distance traveled after time $$t$$?

Accepted Answer

$$x = v_0$ t + \frac{1}{2} a t^2$

Question 3

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

Accepted Answer

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

Question 4

Which formula best describes the work done by a constant force $$F$$ acting over a displacement $$d at an $$angle $$	heta$$?

Accepted Answer

$$W = F d \cos 	heta$$

Question 5

A 5 kg mass is dropped from a height of 10 m. Ignoring air resistance, what is its velocity just before hitting the ground? (Use $$g = 9.8\, 	ext{m/s}^2)$$

Accepted Answer

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

Question 6

Which equation gives the kinetic energy of an object of mass $$m$$ moving at velocity $$v$$?

Accepted Answer

$$KE = \frac{1}{2} m v^2$

Question 7

A spring with spring constant $$k is $$compressed by a distance $$x. $$What is the potential energy stored in the spring?

Accepted Answer

$$U = \frac{1}{2} k x^2$

Question 8

A 3 kg object moving at $$4\, 	ext{m/s}$$ collides with a stationary 2 kg object. If they stick together, what is their final velocity?

Accepted Answer

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

Question 9

Which of the following best describes the center of mass for a system of particles?

Accepted Answer

$$x_{cm} = \frac{\sum m_i x_i}{\sum m_i}$$

Question 10

A rotating disk has a moment of inertia $$I$$ and angular velocity $$\omega. $$What is its rotational kinetic energy?

Accepted Answer

$$KE_{rot} = \frac{1}{2} I \$$omega^2$$

Question 11

A 1 kg ball is thrown vertically upward with an initial velocity of $$10\, 	ext{m/s}. $$What is its maximum height? (Use $$g = 9.8\, 	ext{m/s}^2)$$

Accepted Answer

$$h = \frac{v_0$^2}{2g} = \frac{100}{19.6} \approx 5.1\, 	ext{m}$$

Question 12

Which physical constant is most relevant when calculating the gravitational force between two masses?

Accepted Answer

The gravitational constant $$G$$

Question 13

A cyclist increases her speed from $$5\, 	ext{m/s} to$$ $$15\, 	ext{m/s}$$ over a distance of $$100\, 	ext{m}. $$What is her acceleration, assuming constant acceleration?

Accepted Answer

$$a = \frac{v^2$ - v_0$^2}{2d} = \frac{225 - 25}{200} = 1\, 	ext{m/s}^2$$

Question 14

A 0.5 kg ball moving at $$2\, 	ext{m/s}$$ bounces off a wall and returns at $$-1\, 	ext{m/s}. $$What is the change in momentum?

Accepted Answer

$$\Delta p = m (v_f - v_i) = 0.5 	imes (-1 - 2) = -1.5\, 	ext{kg m/s}$$

Question 15

Which equation represents the conservation of mechanical energy for a system with only conservative forces?

Accepted Answer

$$E_{initial} = E_{final}$$

Question 16

A 10 kg box is pushed across a floor with a force of 50 N at an angle of $$30^\circ to $$the horizontal for 5 m. How much work is done by the force?

Accepted Answer

$$W = F d \cos 	heta = 50 	imes 5 	imes \cos 30^\circ = 216.5\, 	ext{J}$$

Question 17

A rotating wheel slows from $$20\, 	ext{rad/s} to$$ $$0\, 	ext{rad/s} in$$ $$4\, 	ext{s}. $$What is its angular acceleration?

Accepted Answer

$$\alpha = \frac{\omega_f - \omega_i}{t} = \frac{0 - 20}{4} = -5\, 	ext{rad/s}^2$$

Question 18

A 2 kg object is attached to a spring with $$k = 100\, 	ext{N/m}$$ and oscillates with amplitude $$0.1\, 	ext{m}. $$What is its maximum potential energy?

Accepted Answer

$$U_{max} = \frac{1}{2} k x^2$ = \frac{1}{2} 	imes 100 	imes (0.1)^2$ = 0.5\, 	ext{J}$$

PHY2004 Exam 1 Formula Sheet: Physics with Calculus Study Notes

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