Q: A car with a mass of 1200 kg is heading down a $$20^ ext{o}$$ slope on dry concrete. If the coefficient of static friction is $$\mu_s = 0.85$$, what is the maximum deceleration the car can achieve without slipping? (Assume $$g = 9.80\ \text{m/s}^2.)$$

$$a = g(\mu_s \cos 20^\text{o} - \sin 20^\text{o})$$

Q: Convert $$9.80\ \text{m/s}^2 to$$ $$\text{ft/s}^2. ($$Note: $$1\ \text{m} = 39.37\ \text{in}$$, $$1\ \text{ft} = 12\ \text{in})$$

$$9.80 \times \frac{39.37}{12} = 32.1\ \text{ft/s}^2$$

Q: A man with a mass of $$95\ \text{kg}$$ stands on a scale in an elevator moving upward at a constant speed of $$6\ \text{m/s}. $$What does the scale read?

$$95 \times 9.80 = 931\ \text{N}$$

Q: Suppose you are on Mars, where the planet has a mass of $$6.42 \times 10$$^{23}$$\ \text{kg}$$ and a mean radius of $$3.37 \times 10^6$\ \text{m}. $$What is the acceleration due to gravity on Mars?

$$g = \frac{G M}{r^2$}$$, where $$G = 6.67 \times 10$$^{-11}$$\ \text{N}\cdot\text{m}^2/\text{kg}^2$$; $$g = 3.37\ \text{m/s}^2$$

Q: A vector has components $$F_x = -1200\ \text{N}$$ and $$F_y = 600\ \text{N}. $$What is the magnitude and direction of the resultant vector?

Magnitude: $$\sqrt{(-1200)^2$ + 600^2$} = 1341.6\ \text{N}$$; Direction: $$\theta = \arctan\left(\frac{600}{-1200}\right) = -26.6^\text{o}$$

Q: A space suit has a mass of $$136.4\ \text{kg}. $$What is its weight on Earth? (Note: $$1\ \text{kg} = 2.2\ \text{lbs} on $$Earth's surface)

$$136.4 \times 2.2 = 300.08\ \text{lbs}$$

Q: An ant with a mass of $$3.0\ \text{mg} is $$dropped from a $$100\ \text{m}$$ building. Neglecting air resistance, what is its final speed upon impact?

$$v = \sqrt{2gh} = \sqrt{2 \times 9.80 \times 100} = 44.3\ \text{m/s}$$

Q: A man with a mass of $$95\ \text{kg}$$ stands on a scale in an elevator accelerating upward at $$4.3\ \text{m/s}^2. $$What does the scale read?

$$95 \times (9.80 + 4.3) = 1,335.5\ \text{N}$$

Q: Given the equation $$\Sigma F_y = n - mg \cos \theta = ma_y$$, solve for $$a_y.$$

$$a_y = \frac{n - mg \cos \theta}{m}$$

Question 1

A car with a mass of 1200 kg is heading down a $$20^	ext{o}$$ slope on dry concrete. If the coefficient of static friction is $$\mu_s = 0.85$$, what is the maximum deceleration the car can achieve without slipping? (Assume $$g = 9.80\ 	ext{m/s}^2.)$$

Accepted Answer

$$a = g(\mu_s \cos 20^	ext{o} - \sin 20^	ext{o})$$

Question 2

Convert $$9.80\ 	ext{m/s}^2 to$$ $$	ext{ft/s}^2. ($$Note: $$1\ 	ext{m} = 39.37\ 	ext{in}$$, $$1\ 	ext{ft} = 12\ 	ext{in})$$

Accepted Answer

$$9.80 	imes \frac{39.37}{12} = 32.1\ 	ext{ft/s}^2$$

Question 3

A man with a mass of $$95\ 	ext{kg}$$ stands on a scale in an elevator moving upward at a constant speed of $$6\ 	ext{m/s}. $$What does the scale read?

Accepted Answer

$$95 	imes 9.80 = 931\ 	ext{N}$$

Question 4

Suppose you are on Mars, where the planet has a mass of $$6.42 	imes 10$$^{23}$$\ 	ext{kg}$$ and a mean radius of $$3.37 	imes 10^6$\ 	ext{m}. $$What is the acceleration due to gravity on Mars?

Accepted Answer

$$g = \frac{G M}{r^2$}$$, where $$G = 6.67 	imes 10$$^{-11}$$\ 	ext{N}\cdot	ext{m}^2/	ext{kg}^2$$; $$g = 3.37\ 	ext{m/s}^2$$

Question 5

A vector has components $$F_x = -1200\ 	ext{N}$$ and $$F_y = 600\ 	ext{N}. $$What is the magnitude and direction of the resultant vector?

Accepted Answer

Magnitude: $$\sqrt{(-1200)^2$ + 600^2$} = 1341.6\ 	ext{N}$$; Direction: $$	heta = \arctan\left(\frac{600}{-1200}ight) = -26.6^	ext{o}$$

Question 6

A space suit has a mass of $$136.4\ 	ext{kg}. $$What is its weight on Earth? (Note: $$1\ 	ext{kg} = 2.2\ 	ext{lbs} on $$Earth's surface)

Accepted Answer

$$136.4 	imes 2.2 = 300.08\ 	ext{lbs}$$

Question 7

An ant with a mass of $$3.0\ 	ext{mg} is $$dropped from a $$100\ 	ext{m}$$ building. Neglecting air resistance, what is its final speed upon impact?

Accepted Answer

$$v = \sqrt{2gh} = \sqrt{2 	imes 9.80 	imes 100} = 44.3\ 	ext{m/s}$$

Question 8

A man with a mass of $$95\ 	ext{kg}$$ stands on a scale in an elevator accelerating upward at $$4.3\ 	ext{m/s}^2. $$What does the scale read?

Accepted Answer

$$95 	imes (9.80 + 4.3) = 1,335.5\ 	ext{N}$$

Question 9

If a person wants to increase their weight without changing their mass, what could they do?

Accepted Answer

Travel to a planet with higher gravitational acceleration.

Question 10

Given the equation $$\Sigma F_y = n - mg \cos 	heta = ma_y$$, solve for $$a_y.$$

Accepted Answer

$$a_y = \frac{n - mg \cos 	heta}{m}$$

Question 11

A spherical drop of jet fuel has diameter $$d$$ and density $$\rho. $$What is its mass?

Accepted Answer

$$m = \rho \left( \frac{4}{3} \pi \left( \frac{d}{2} \$$right)^3$$ \right)$$

Question 12

Which of the following best describes Newton's 3rd Law?

Accepted Answer

For every action, there is an equal and opposite reaction.

Question 13

Two vectors are given: $$\langle 410\ 	ext{N}, 111^	ext{o} angle$$ and $$\langle 683\ 	ext{N}, 280^	ext{o} angle. $$What is the magnitude of their sum?

Accepted Answer

$$\sqrt{(410 \cos 111^	ext{o} + 683 \cos 280^	ext{o})^2$ + (410 \sin 111^	ext{o} + 683 \sin 280^	ext{o})^2$}$$

Question 14

A $$30\ 	ext{kg}$$ mass is acted upon by forces: $$300\ 	ext{N}$$ right, $$200\ 	ext{N}$$ left, $$150\ 	ext{N} up$$, $$100\ 	ext{N}$$ down. What is the net force?

Accepted Answer

$$100\ 	ext{N}$$ right, $$50\ 	ext{N} up$$

Question 15

A mass $$m_1 = 51$$\ 	ext{kg}$$ moves upward on a frictionless pulley system, while m_2$ = 101\ 	ext{kg}$$ moves downward. What is the acceleration of $$m_1$$? (Neglect friction and assume $$g = 9.80\ 	ext{m/s}^2.)$$

Accepted Answer

$$a = \frac{m_2$ - m_1$}{m_1$ + m_2$} g$$

Question 16

A $$9\ 	ext{kg}$$ object is moving to the right with a force of $$12\ 	ext{N}$$ applied. If the coefficient of friction is $$\mu = 0.41$$ and $$g = 9.80\ 	ext{m/s}^2$$, what is the acceleration?

Accepted Answer

$$a = \frac{12 - (0.41 	imes 9 	imes 9.80)}{9}$$

Question 17

If the cable breaks in an elevator and the elevator is in free fall, what does the scale read for a $$95\ 	ext{kg}$$ person?

Accepted Answer

Zero; the person is weightless.

Question 18

Which of the following is NOT a consequence of Newton's 1st Law?

Accepted Answer

For every action, there is an equal and opposite reaction.

Physics with Calculus: Step-by-Step Guidance for Test 2 Review

Study Guide - Practice Questions

Study Guide - Flashcards