Q: Which of the following is the correct vector decomposition for $$\vec{T}_B if it $$makes an angle $$\theta$$ with the vertical?

$$T_B \sin \theta \hat{i} + T_B \cos \theta \hat{j}$$

Q: A 550 N student stands on a scale in an elevator. The combined mass of student and elevator is 850 kg. If the scale reads 450 N, what is the tension in the cable supporting the elevator?

$$T = (850\ \mathrm{kg}) \times (9.8\ \mathrm{m/s^2$}) - (550\ \mathrm{N} - 450\ \mathrm{N})$$

Question 1

An elevator is being lowered at a constant speed by a steel cable. There is no air resistance or friction. What is the upward force exerted on the elevator by the cable?

Accepted Answer

It is equal to the force of gravity.

Question 2

A wrecking ball of mass $$m = 3470\ \mathrm{kg} is $$suspended by a cable that makes an angle of $$40.0^\circ$$ with the vertical. What is the tension $$T_B in $$the cable?

Accepted Answer

$$T_B = \dfrac{mg}{\cos 40.0^\circ}$$

Question 3

A 550 N physics student stands on a bathroom scale in an elevator. The scale reads 450 N as the elevator starts moving. What is the acceleration of the elevator? (Take $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$a = -1.79\ \mathrm{m/s^2$}$$

Question 4

A toboggan loaded with students slides down a frictionless hill at angle $$	heta. $$What is the acceleration of the toboggan?

Accepted Answer

$$a = g \sin 	heta$$

Question 5

A 25.0 N weight is suspended at each end of a rope over a frictionless pulley. What is the tension in the rope?

Accepted Answer

$$25.0\ \mathrm{N}$$

Question 6

A 550 N student stands on a scale in an elevator. If the scale reads zero, what does this indicate?

Accepted Answer

The elevator is in free fall.

Question 7

The bathroom scale in an elevator measures:

Accepted Answer

The normal force exerted by the floor.

Question 8

If the tension in the cable supporting an elevator is less than the weight of the elevator, what happens?

Accepted Answer

The elevator accelerates downward.

Question 9

A wrecking ball is held in equilibrium by two cables. If $$T_A is $$the horizontal tension and $$T_B$$ makes an angle $$	heta$$ with the vertical, what is the $$y-$$component of $$T_B$$?

Accepted Answer

$$T_B \cos 	heta$$

Question 10

A 550 N student stands on a scale in an elevator. The scale reads 670 N. What is the acceleration of the elevator?

Accepted Answer

$$a = 2.14\ \mathrm{m/s^2$}$$\ upward

Question 11

Which equation correctly represents Newton’s Second Law for the net force in the $$y-$$direction for the wrecking ball system?

Accepted Answer

$$0 = T_B \cos 	heta - mg$$

Question 12

A 25.0 N weight is suspended at each end of a rope over a frictionless pulley. What is the tension in the chain holding the pulley?

Accepted Answer

$$50.0\ \mathrm{N}$$

Question 13

A toboggan slides down a hill at angle $$	heta$$ with negligible friction. If the total weight is $$W$$, what is the net force down the slope?

Accepted Answer

$$W \sin 	heta$$

Question 14

If a bathroom scale reads higher than your actual weight while in an elevator, what does this indicate?

Accepted Answer

The elevator is accelerating upward.

Question 15

Which of the following is the correct vector decomposition for $$\vec{T}_B if it $$makes an angle $$	heta$$ with the vertical?

Accepted Answer

$$T_B \sin 	heta \hat{i} + T_B \cos 	heta \hat{j}$$

Question 16

A 550 N student stands on a scale in an elevator. The combined mass of student and elevator is 850 kg. If the scale reads 450 N, what is the tension in the cable supporting the elevator?

Accepted Answer

$$T = (850\ \mathrm{kg}) 	imes (9.8\ \mathrm{m/s^2$}) - (550\ \mathrm{N} - 450\ \mathrm{N})$$

Question 17

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

Accepted Answer

The object is either at rest or moving at constant velocity.

Question 18

A student of mass $$m$$ stands on a scale in an elevator. If the elevator accelerates downward with acceleration $$a$$, what does the scale read?

Accepted Answer

$$m(g-a)$$

Applications of Newton’s Laws: Equilibrium, Tension, and Apparent Weight

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