Question 1

A 100 N traffic light is suspended by two cables making angles $$\$$theta_1$$ = 70^\circ$$ and $$\$$theta_2$$ = 30^\circ$$ with the horizontal. What is the tension $$T_1 in $$the cable at $$70^\circ$$?

Accepted Answer

$$T_1 = 87.94$$\ \mathrm{N}$$

Question 2

For the same traffic light scenario, what is the tension $$T_2 in $$the cable at $$30^\circ$$?

Accepted Answer

$$T_2 = 34.73$$\ \mathrm{N}$$

Question 3

In the traffic light problem, which variable(s) affect the ratio $$T_2$$/$$T_1$$?

Accepted Answer

Only the angles $$\$$theta_1$$ and $$\$$theta_2$$

Question 4

Why is it not a problem that the algebraic sum $$T_1$$ + $$T_2 is $$greater than the weight $$W in $$the traffic light scenario?

Accepted Answer

Because the vector sum of $$T_1$$ and $$T_2$$ equals $$W$$

Question 5

A 10 kg box is held motionless on a frictionless incline of $$30^\circ. A $$force $$P is $$applied at a downward angle of $$18^\circ$$ below the horizontal. What is the value of $$P$$ required to just hold the box stationary?

Accepted Answer

$$P = 73.23\ \mathrm{N}$$

Question 6

If the force $$P$$ from the previous question is doubled, what is the acceleration of the box and in which direction?

Accepted Answer

$$a = 4.9\ \mathrm{m/s}^2 up $$the incline

Question 7

If the force $$P is $$halved from the value needed to hold the box stationary, what is the acceleration of the box and in which direction?

Accepted Answer

$$a = 2.45\ \mathrm{m/s}^2$$ down the incline

Question 8

In the box-on-incline problem, what is the component of the gravitational force parallel to the incline?

Accepted Answer

$$W_x = mg \sin(30^\circ) = 49\ \mathrm{N}$$

Question 9

Which of the following best explains why the $$y-$$component of the push force $$P is $$not needed to determine the force required to keep the box stationary on the incline?

Accepted Answer

Because only the $$x-$$component of $$P ($$parallel to the incline) opposes the component of gravity down the incline

Question 10

If the angle of the incline is increased while keeping the mass and push force direction the same, what happens to the required magnitude of $$P to $$keep the box stationary?

Accepted Answer

It increases

Question 11

Suppose the mass of the box is doubled but the incline angle and push direction remain unchanged. What happens to the required push force $$P to $$keep the box stationary?

Accepted Answer

It doubles

Question 12

In the traffic light problem, if $$\$$theta_1$$ is increased and $$\$$theta_2 is $$decreased (keeping $$W$$ constant), what happens to the ratio $$T_2$$/$$T_1$$?

Accepted Answer

It increases

Question 13

A student claims that the sum of the magnitudes of the tensions in the cables must always equal the weight of the traffic light. Is this correct?

Accepted Answer

No, because only the vector sum of the tensions equals the weight

Question 14

If the push force $$P on $$the box is applied at a greater downward angle (more below the horizontal), what happens to the $$x-$$component of $$P ($$parallel to the incline)?

Accepted Answer

It decreases

Question 15

A 10 kg box is on a frictionless $$30^\circ$$ incline. If no force is applied, what is the acceleration of the box down the incline?

Accepted Answer

$$a = 4.9\ \mathrm{m/s}^2$$ down the incline

Question 16

In the traffic light problem, if the weight $$W is $$increased but the angles remain the same, what happens to the tensions $$T_1$$ and $$T_2$$?

Accepted Answer

Both $$T_1$$ and $$T_2$$ increase proportionally

Physics Study Notes: Forces, Equilibrium, and Inclined Planes

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