Q: 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, holding it steady. What force must the man apply? (Assume $$g = 9.8\ \mathrm{m/s^2$})$$

$$F_m = \frac{910 \times 9.8 \times 0.85}{3.6} = 2120\ \mathrm{N}$$

Q: A 61 kg woman stands on tiptoe on one foot. The upward force from the floor acts 0.15 m from the ankle pivot, and the Achilles tendon acts 0.05 m from the pivot. What is the tension in the tendon?

$$T = 3 \times (61 \times 9.8) = 1794\ \mathrm{N}$$

Question 1

Which of the following conditions must be satisfied 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, holding it steady. What force must the man apply? (Assume $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$F_m = \frac{910 	imes 9.8 	imes 0.85}{3.6} = 2120\ \mathrm{N}$$

Question 3

Which of the following statements about torque and equilibrium is correct?

Accepted Answer

Both the net force and the net torque must be zero for static equilibrium.

Question 4

A ladder leans against a wall at a $$60^\circ$$ angle with the floor. If the coefficient of static friction between the ladder and the ground is $$\mu_s = 0.29$$, will the ladder slip?

Accepted Answer

No, because $$\mu_s is $$greater than the minimum required value.

Question 5

Why is it advantageous to choose the pivot point at the location where forces are poorly specified when calculating torque?

Accepted Answer

It eliminates the torque due to those forces, simplifying calculations.

Question 6

A 2-m-long board weighing 50 N extends over the edge of a table, with 40% of its length off the table. How far beyond the table edge can a 25-N cat walk before the board begins to tilt?

Accepted Answer

0.6 m

Question 7

Which of the following increases the stability of an object?

Accepted Answer

A lower center of gravity and a wider base of support.

Question 8

A spring stretches from 20 cm to 22 cm when pulled with a force of 100 N. What is the spring constant $$k$$?

Accepted Answer

$$k = \frac{100}{0.02} = 5000\ \mathrm{N/m}$$

Question 9

Which spring has the largest spring constant?

Accepted Answer

The spring with the steepest slope on a force vs. displacement graph.

Question 10

A steel cable of length $$L = 6.0\ \mathrm{m}$$ and diameter $$d = 2.5\ \mathrm{mm}$$ supports a $$120\ \mathrm{kg}$$ mass. Given Young’s modulus for steel $$Y = 2.0 	imes 10$$^{11}$$\ \mathrm{N/m^2$}$$, by how much does the cable stretch? ($$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$\Delta L = \frac{F L}{A Y}$$, where $$F = mg$$ and $$A = \pi (d/2)^2$

Question 11

A 61 kg woman stands on tiptoe on one foot. The upward force from the floor acts 0.15 m from the ankle pivot, and the Achilles tendon acts 0.05 m from the pivot. What is the tension in the tendon?

Accepted Answer

$$T = 3 	imes (61 	imes 9.8) = 1794\ \mathrm{N}$$

Question 12

Which of the following best describes the mechanical advantage of a lever?

Accepted Answer

It is the ratio of the output force to the input force.

Question 13

A rod is stretched by a force $$F. $$The restoring force can be written in terms of stress and strain as:

Accepted Answer

$$	ext{Stress} = Y 	imes 	ext{Strain}$$

Question 14

Bars A and B are attached to a wall and pulled with equal forces. Bar B has twice the radius and is stretched half as far as bar A. Which has the larger Young’s modulus?

Accepted Answer

Bar A

Question 15

What happens to a material when the applied stress exceeds its ultimate stress?

Accepted Answer

The material breaks.

Question 16

A car is less likely to roll over if:

Accepted Answer

The center of gravity is low and the track width is wide.

Question 17

Which of the following is true about the elastic limit of a material?

Accepted Answer

It is the maximum stretch for which the material returns to its original length when the force is removed.

Question 18

A spring with $$k = 125\ \mathrm{N/m}$$ pulls a 25 N block across a table with friction. If the coefficient of friction is $$\mu = 0.2$$, how much does the spring stretch?

Accepted Answer

$$\Delta x = \frac{\mu F_N}{k} = \frac{0.2 	imes 25}{125} = 0.04\ \mathrm{m}$$

Chapter 8: Equilibrium and Elasticity – Physics with Calculus Study Notes

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