Q: A 510 kg safe is to be moved up a ramp inclined at $$15^\circ$$ with a coefficient of static friction $$\mu_s = 0.42. $$What is the minimum force parallel to the incline required to start moving the safe?

$$F = mg \sin \theta + \mu_s mg \cos \theta$$

Question 1

Which of the following statements best distinguishes a scalar from a vector quantity?

Accepted Answer

A scalar has only magnitude, while a vector has both magnitude and direction.

Question 2

A force vector $$\vec{F}$$ has a magnitude of 9.4 N and is directed $$58^\circ$$ below the $$+x-$$axis. What are the $$x$$ and $$y$$ components of this force?

Accepted Answer

$$F_x = 9.4 \cos 58^\circ$$, $$F_y = -9.4 \sin 58^\circ$$

Question 3

Given two forces, $$\vec{A} = 475\ \mathrm{N}$$ due west and $$\vec{B} = 315\ \mathrm{N}$$ due south, what is the magnitude of the single force that would have the same effect as both forces combined?

Accepted Answer

$$\sqrt{475^2$ + 315^2$}\ \mathrm{N}$$

Question 4

Which of the following is NOT a fundamental force in nature?

Accepted Answer

Normal force

Question 5

A box weighing 750 N is pushed across a horizontal floor at constant velocity with a force of 450 N. What is the coefficient of kinetic friction between the box and the floor?

Accepted Answer

$$\mu_k = \frac{450}{750}$$

Question 6

A car is parked on a ramp inclined at an angle $$	heta$$ with the ground. Which force is responsible for keeping the car stationary?

Accepted Answer

Static friction

Question 7

If a vector $$\vec{C}$$ has components $$C_x = -450\ \mathrm{N}$$ and $$C_y = 750\ \mathrm{N}$$, what is the magnitude of $$\vec{C}$$?

Accepted Answer

$$\sqrt{(-450)^2$ + (750)^2$}\ \mathrm{N}$$

Question 8

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

Accepted Answer

An object’s velocity vector remains constant if and only if the net force acting on the object is zero.

Question 9

A 20 kg sphere is placed 3 cm from another 20 kg sphere. What is the gravitational force between them? (Use $$G = 6.674 	imes 10$$^{-11}$$\ \mathrm{N\cdot m^2$/kg^2$$}$)

Accepted Answer

$$F = G \frac{m_1$ m_2$}{r^2$}$$

Question 10

A deltoid muscle exerts a force of 270 N at an angle of $$15^\circ$$ above the horizontal on the humerus. What is the $$y-$$component of this force?

Accepted Answer

$$F_y = 270 \sin 15^\circ$$

Question 11

Which equation correctly expresses the relationship between the percentage change $$n$$ and the final value $$E_f of a $$quantity $$E_0$$ that increases by $$n\%$$?

Accepted Answer

$$E_f = E_0$ \left(1 + \frac{n}{100}\right)$$

Question 12

A 510 kg safe is to be moved up a ramp inclined at $$15^\circ$$ with a coefficient of static friction $$\mu_s = 0.42. $$What is the minimum force parallel to the incline required to start moving the safe?

Accepted Answer

$$F = mg \sin 	heta + \mu_s mg \cos 	heta$$

Question 13

Which of the following is true about the tension in an ideal cord passing through an ideal pulley?

Accepted Answer

The tension is the same on both sides of the pulley.

Question 14

A box is at rest on a rough inclined plane. Which forces act on the box?

Accepted Answer

Weight, normal force, and friction

Question 15

If the net force acting on an object is zero, which of the following must be true?

Accepted Answer

The object is in equilibrium and its acceleration is zero.

Question 16

Which of the following best describes the normal force?

Accepted Answer

The component of the contact force perpendicular to the surface.

Question 17

A car is moving eastward with a thrust of 1.8 kN and a drag of 0.8 kN west. What is the net force in the $$x-$$direction?

Accepted Answer

$$1.0\ \mathrm{kN}$$ east

Question 18

Which equation gives the maximum static friction force?

Accepted Answer

$$f_{s,\mathrm{max}} = \mu_s N$$

Question 19

Which of the following is a correct statement of Newton’s Third Law?

Accepted Answer

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

Vectors and Forces: Foundations of Physics

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