Q: A car has a track width $$t$$ and a center-of-gravity height $$h. $$The critical angle $$\theta_c at $$which it will tip is given by:

$$\tan \theta_c = \frac{t}{2h}$$

Question 1

Which of the following is a necessary condition for an 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 person lifts the beam at its end, 3.6 m from the pivot, holding it steady. What force must the person apply? (Assume $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$2100\ \mathrm{N}$$

Question 3

Why is it often advantageous to choose the pivot point at the location where forces are poorly specified when solving static equilibrium problems?

Accepted Answer

It eliminates the need to consider those forces in the torque equation.

Question 4

A 3.0-m ladder leans against a wall at $$60^\circ to $$the floor. What is the minimum coefficient of static friction $$\mu_s at $$the ground to prevent slipping? (Assume friction at the wall is negligible.)

Accepted Answer

$$0.29$$

Question 5

A uniform 5.0-m ladder of mass $$12.0\ \mathrm{kg}$$ leans against a frictionless wall, touching the wall 4.0 m above the floor. What is the horizontal force exerted by the wall on the ladder?

Accepted Answer

$$44.1\ \mathrm{N}$$

Question 6

Which of the following best describes stable equilibrium?

Accepted Answer

An object returns to its equilibrium position after being slightly displaced.

Question 7

A car has a track width $$t$$ and a center-of-gravity height $$h. $$The critical angle $$	heta_c at $$which it will tip is given by:

Accepted Answer

$$	an 	heta_c = \frac{t}{2h}$$

Question 8

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

Accepted Answer

0.8 m

Question 9

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 10

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

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

Question 11

A 120 kg steel ball hangs from a 6.0-m-long steel cable with a diameter of 2.5 mm. 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 m

Question 12

Which material has the highest Young’s modulus among the following?

Accepted Answer

Steel

Question 13

A tendon in the human body is stretched by a force of 1000 N. If its cross-sectional area is $$5 	imes 10$$^{-6}$$\ \mathrm{m^2$}$$ and its original length is 0.1 m, and Young’s modulus is $$1.5 	imes 10^9$\ \mathrm{N/m^2$}$$, what is the change in length?

Accepted Answer

0.0013 m

Question 14

Which of the following best describes the elastic limit of a material?

Accepted Answer

The maximum stress the material can withstand before permanent deformation.

Question 15

A 61 kg woman stands on tiptoe, with the sole of her foot making a $$25^\circ$$ angle with the floor. If the upward force from the floor is 600 N at 0.15 m from the ankle pivot and the Achilles tendon force acts at 0.05 m, what is the tension in the tendon?

Accepted Answer

1800 N

Question 16

Which of the following increases the stability of an object?

Accepted Answer

Lowering the center of gravity and widening the base of support.

Question 17

A spring with $$k = 125\ \mathrm{N/m} is $$used to pull a 25 N block across a table with friction coefficient $$\mu = 0.2. By $$how much does the spring stretch?

Accepted Answer

0.04 m

Question 18

Which of the following statements about mechanical advantage is correct?

Accepted Answer

Mechanical advantage allows a smaller force to apply a larger force at a different point using leverage.

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