Question 1

A vector $$\vec{A}$$ has a magnitude of $$10\ \mathrm{N}$$ and points at an angle of $$30^\circ$$ above the positive x-axis. What are the x- and y-components of $$\vec{A}$$?

Accepted Answer

$$A_x = 10 \cos 30^\circ = 8.66\ \mathrm{N},\ A_y = 10 \sin 30^\circ = 5.0\ \mathrm{N}$$

Question 2

Which of the following statements about Newton's Third Law is correct?

Accepted Answer

The forces in a third law pair act on different objects and are equal in magnitude but opposite in direction.

Question 3

A 70 kg person stands on a scale in an elevator accelerating upward at $$2\ \mathrm{m/s^2$}. $$What does the scale read?

Accepted Answer

$$840\ \mathrm{N}$$

Question 4

A mosquito collides head-on with a truck. According to Newton's Third Law, during the collision:

Accepted Answer

The force exerted by the mosquito on the truck is equal in magnitude and opposite in direction to the force exerted by the truck on the mosquito.

Question 5

If a vector $$\vec{B}$$ has components $$B_x = 3\ \mathrm{m}$$ and $$B_y = 4\ \mathrm{m}$$, what is the magnitude of $$\vec{B}$$?

Accepted Answer

$$5\ \mathrm{m}$$

Question 6

A block is pulled by two ropes: Rope 1 exerts a force of $$500\ \mathrm{N} to $$the right, and Rope 2 exerts a force of $$400\ \mathrm{N} to $$the left. What is the net force on the block?

Accepted Answer

$$100\ \mathrm{N} to $$the right

Question 7

Which trigonometric function would you use to find the x-component of a vector given its magnitude and the angle $$	heta$$ measured from the x-axis?

Accepted Answer

$$\cos 	heta$$

Question 8

A person stands on a scale in a stationary elevator. The scale reads 600 N. If the elevator suddenly accelerates downward at $$2\ \mathrm{m/s^2$}$$, what does the scale read? (Assume $$g = 10\ \mathrm{m/s^2$}.)$$

Accepted Answer

$$480\ \mathrm{N}$$

Question 9

Which of the following best describes the 'tip-to-tail' method for vector addition?

Accepted Answer

Placing the tail of each subsequent vector at the head of the previous vector and drawing the resultant from the tail of the first to the head of the last vector.

Question 10

A force $$\vec{F}$$ has components $$F_x = -6\ \mathrm{N}$$ and $$F_y = 8\ \mathrm{N}. $$What is the direction of $$\vec{F}$$ relative to the positive x-axis?

Accepted Answer

$$127^\circ$$

Question 11

If a vector $$\vec{C} is $$multiplied by a scalar $$-3$$, what happens to its magnitude and direction?

Accepted Answer

The magnitude is multiplied by 3 and the direction is reversed.

Question 12

A 10 kg box is at rest on a horizontal surface. The normal force acting on the box is:

Accepted Answer

$$98\ \mathrm{N}$$ upward

Question 13

Which of the following is a correct application of Newton's Second Law in two dimensions?

Accepted Answer

$$\sum F_x = m a_x$$ and $$\sum F_y = m a_y$$

Question 14

A student pushes a box across a frictionless floor with a force of $$20\ \mathrm{N} at$$ $$60^\circ$$ above the horizontal. What is the horizontal component of the force?

Accepted Answer

$$20 \cos 60^\circ = 10\ \mathrm{N}$$

Question 15

Which of the following is NOT a property of vectors?

Accepted Answer

Vectors can be multiplied by a scalar to change their direction and magnitude, but not both at the same time.

Question 16

A 5 kg object is suspended by a rope. What is the tension in the rope if the object is at rest?

Accepted Answer

$$49\ \mathrm{N}$$

Question 17

If you stand on a scale in a freely falling elevator, what will the scale read?

Accepted Answer

Zero

Question 18

Which of the following best describes the difference between mass and weight?

Accepted Answer

Mass is a measure of the amount of matter in an object, while weight is the force due to gravity acting on that mass.

Question 19

A force of $$F = 10\ \mathrm{N}$$ acts at an angle of $$45^\circ$$ above the x-axis. What is the y-component of the force?

Accepted Answer

$$10 \sin 45^\circ = 7.07\ \mathrm{N}$$

Physics 201: Vectors, Forces, and Newton's Laws in Two Dimensions

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