Q: A ladder leans against a wall at $$60^\circ to $$the ground. What is the minimum coefficient of static friction $$\mu$$ required to prevent slipping?

$$\mu = \frac{1}{2} \tan 60^\circ$$

Q: A car has a track width $$t$$ and center of gravity height $$h. $$What is the critical angle $$\theta_c at $$which the car will tip over?

$$\theta_c = \tan$$^{-1}$$\left(\frac{t}{2h}\right)$$

Question 1

Which of the following is a necessary condition for an extended object to be in static equilibrium?

Accepted Answer

Both the net force and the net torque on the object must be zero.

Question 2

A 910 kg bucket is suspended 0.85 m from a pivot on a beam. A man lifts the beam at its end, 3.6 m from the pivot, keeping it steady. What force must the man apply to hold the beam in equilibrium? (Assume $$g = 9.8 \mathrm{\ m/s^2$})$$

Accepted Answer

$$2100 \mathrm{\ N}$$

Question 3

If the net force on a block is zero but the net torque is not zero, what will happen to the block?

Accepted Answer

The block will not be in static equilibrium and will rotate.

Question 4

A uniform 50 N board extends over the edge of a table, with 40% of its length on the table. How far beyond the table edge can a 5 kg cat walk before the board begins to tilt? (Assume $$g = 9.8 \mathrm{\ m/s^2$}$$ and the board is 2 m long.)

Accepted Answer

$$0.4 \mathrm{\ m}$$

Question 5

Which of the following best describes the effect of a wider base of support and a lower center of gravity on the stability of an object?

Accepted Answer

It increases the stability of the object.

Question 6

A 20 cm spring is stretched to 22 cm by a force of 100 N. What is the spring constant $$k$$?

Accepted Answer

$$5000 \mathrm{\ N/m}$$

Question 7

A steel cable of length $$6.0 \mathrm{\ m}$$ and diameter $$2.5 \mathrm{\ mm}$$ supports a $$120 \mathrm{\ kg}$$ ball. If Young's modulus for steel is $$2.0 	imes 10$$^{11}$$ \mathrm{\ N/m^2$}$$, by how much does the cable stretch?

Accepted Answer

$$0.0072 \mathrm{\ m}$$

Question 8

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

Accepted Answer

The restoring force is proportional to the displacement and acts in the opposite direction.

Question 9

A ladder leans against a wall at $$60^\circ to $$the ground. What is the minimum coefficient of static friction $$\mu$$ required to prevent slipping?

Accepted Answer

$$\mu = \frac{1}{2} 	an 60^\circ$$

Question 10

A car has a track width $$t$$ and center of gravity height $$h. $$What is the critical angle $$	heta_c at $$which the car will tip over?

Accepted Answer

$$	heta_c = 	an$$^{-1}$$\left(\frac{t}{2h}ight)$$

Question 11

A spring with $$k = 125 \mathrm{\ N/m}$$ pulls a $$25 \mathrm{\ N}$$ block across a tabletop. If the coefficient of friction is $$0.30$$, how much does the spring stretch from equilibrium?

Accepted Answer

$$0.075 \mathrm{\ m}$$

Question 12

Which of the following is true about the mechanical advantage of a lever?

Accepted Answer

Mechanical advantage is the ratio of output force to input force.

Question 13

A woman stands on tiptoe, exerting a force of $$600 \mathrm{\ N} on $$the floor. The Achilles tendon acts $$0.05 \mathrm{\ m}$$ from the pivot, and the floor force acts $$0.15 \mathrm{\ m}$$ from the pivot. What is the tension in the tendon?

Accepted Answer

$$1800 \mathrm{\ N}$$

Question 14

Which of the following materials is most likely to be classified as 'pliant'?

Accepted Answer

Rubber band

Question 15

Young's modulus $$Y is $$defined as:

Accepted Answer

$$Y = \frac{F/A}{\Delta L/L}$$

Question 16

A bar B has twice the radius of bar A and is stretched half as far as bar A under the same force. Which has the larger Young's modulus?

Accepted Answer

Both have the same Young's modulus

Question 17

Which of the following statements about the elastic limit is correct?

Accepted Answer

A rod will return to its original length only if the stretch is less than the elastic limit.

Question 18

In the human body, why is the Achilles tendon force greater than the weight supported when standing on tiptoe?

Accepted Answer

Because the tendon is attached closer to the pivot than the weight force.

Question 19

If the center of gravity of an object moves outside its base of support, what happens?

Accepted Answer

The object becomes unstable and may tip over.

Chapter 8: Equilibrium and Elasticity – Torque and Static Equilibrium

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