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 $$\mu_s = 0.75$$, 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: $$1\ \text{m} = 39.37\ \text{in}$$, $$1\ \text{ft} = 12\ \text{in})$$

$$9.80\ \text{m/s}^2 = 32.2\ \text{ft/s}^2$$

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

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

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

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

Q: Two forces act on a $$30\ \text{kg}$$ mass: $$300\ \text{N} to $$the right and $$200\ \text{N} to $$the left. What is the net force and acceleration?

Net force: $$100\ \text{N}$$ right; Acceleration: $$a = \dfrac{100}{30} = 3.33\ \text{m/s}^2$$

Q: A cable tension has components $$T_x = 410\ \text{N} at$$ $$111^\text{o}$$ and $$T_y = 683\ \text{N} at$$ $$280^\text{o}. $$What is the resultant vector’s magnitude and direction?

Magnitude: $$\sqrt{(410 \cos 111^\text{o} + 683 \cos 280^\text{o})^2$ + (410 \sin 111^\text{o} + 683 \sin 280^\text{o})^2$}$$; Direction: $$\arctan\left(\dfrac{\text{total } y}{\text{total } x}\right)$$

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 $$\mu_s = 0.75$$, 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

$$9.80\ 	ext{m/s}^2 = 32.2\ 	ext{ft/s}^2$$

Question 3

A space suit has a mass of $$136.4\ 	ext{kg}. $$What is its weight on Mars, where $$g_{Mars} is $$calculated using $$M_{Mars} = 6.42 	imes 10$$^{23}$$\ 	ext{kg}$$ and $$R_{Mars} = 3.37 	imes 10^6$\ 	ext{m}$$? ($$G = 6.674 	imes 10$$^{-11}$$\ 	ext{N}\cdot	ext{m}^2/	ext{kg}^2)$$

Accepted Answer

$$W = m \cdot g_{Mars}$$, where $$g_{Mars} = \dfrac{G M_{Mars}}{R_{Mars}^2}$$

Question 4

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

Accepted Answer

$$F_{scale} = m(g + a)$$

Question 5

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

Accepted Answer

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

Question 6

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

Accepted Answer

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

Question 7

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

Accepted Answer

Travel to a planet with stronger gravity.

Question 8

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

Accepted Answer

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

Question 9

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

Accepted Answer

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

Question 10

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

Accepted Answer

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

Question 11

Two forces act on a $$30\ 	ext{kg}$$ mass: $$300\ 	ext{N} to $$the right and $$200\ 	ext{N} to $$the left. What is the net force and acceleration?

Accepted Answer

Net force: $$100\ 	ext{N}$$ right; Acceleration: $$a = \dfrac{100}{30} = 3.33\ 	ext{m/s}^2$$

Question 12

A cable tension has components $$T_x = 410\ 	ext{N} at$$ $$111^	ext{o}$$ and $$T_y = 683\ 	ext{N} at$$ $$280^	ext{o}. $$What is the resultant vector’s magnitude and direction?

Accepted Answer

Magnitude: $$\sqrt{(410 \cos 111^	ext{o} + 683 \cos 280^	ext{o})^2$ + (410 \sin 111^	ext{o} + 683 \sin 280^	ext{o})^2$}$$; Direction: $$\arctan\left(\dfrac{	ext{total } y}{	ext{total } x}ight)$$

Question 13

A mass $$m_1 = 51$$\ 	ext{kg}$$ moves upward on a frictionless pulley system, while m_2$ = 101\ 	ext{kg}$$ moves down an incline of $$72^	ext{o}$$ with $$\mu = 0.14. $$What is the acceleration of $$m_1$$?

Accepted Answer

$$a = \dfrac{m_2$ g \sin 	heta - \mu m_2$ g \cos 	heta - m_1$ g}{m_1$ + m_2$}$$

Question 14

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

Accepted Answer

Zero; the man is in free fall and experiences weightlessness.

Question 15

A $$300\ 	ext{lb}$$ object is converted to Newtons. (Note: $$1\ 	ext{lb} = 4.45\ 	ext{N}.) $$What is its weight in Newtons?

Accepted Answer

$$300 	imes 4.45 = 1335\ 	ext{N}$$

Question 16

Which scenario best illustrates Newton’s 1st Law?

Accepted Answer

A book remains at rest on a table until someone pushes it.

Question 17

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 its acceleration?

Accepted Answer

$$a = \dfrac{12 - \mu m g}{m}$$

Question 18

What is the speed required for a spacecraft to maintain a circular orbit $$50\ 	ext{km}$$ above Mars’ surface? ($$R_{Mars} = 3.37 	imes 10^6$\ 	ext{m}$$, $$M_{Mars} = 6.42 	imes 10$$^{23}$$\ 	ext{kg}$$, $$G = 6.674 	imes 10$$^{-11}$$\ 	ext{N}\cdot	ext{m}^2/	ext{kg}^2)$$

Accepted Answer

$$v = \sqrt{\dfrac{G M_{Mars}}{R_{Mars} + 50,000}}$$

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