Question 1

A uniform 4 m long bar of mass 10 kg is supported at a fulcrum 1 m from its left end. What force must be applied vertically downward at the left edge to keep the bar in equilibrium? (Assume $$g = 10 \ \mathrm{m/s^2$})$$

Accepted Answer

$$75 \ \mathrm{N}$$

Question 2

Which of the following is necessary for a rigid body to be in static equilibrium?

Accepted Answer

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

Question 3

A composite disc consists of two concentric cylinders: the inner radius is $$0.3 \ \mathrm{m}$$ and the outer radius is $$0.5 \ \mathrm{m}. If $$you pull with $$100 \ \mathrm{N} on a $$rope attached to the outer edge, what force must you apply to a rope on the inner edge to prevent rotation?

Accepted Answer

$$60 \ \mathrm{N}$$

Question 4

A 20 kg, 3 m-long bar is held horizontally against a wall by a pin at one end. What is the magnitude of the torque the pin must provide to hold the bar horizontally? (Assume $$g = 10 \ \mathrm{m/s^2$})$$

Accepted Answer

$$100 \ \mathrm{N \cdot m}$$

Question 5

A 4 m-long seesaw of mass $$50 \ \mathrm{kg} is $$pivoted at its center. A $$30 \ \mathrm{kg}$$ child sits at the left edge. How far from the fulcrum should a $$40 \ \mathrm{kg}$$ child sit on the right to balance the seesaw?

Accepted Answer

$$2.25 \ \mathrm{m}$$

Question 6

A 20 kg, 5 m-long bar is suspended from the ceiling by a string attached $$2 \ \mathrm{m}$$ from the right edge. To balance the bar horizontally, what mass $$m$$ should be placed at the right edge?

Accepted Answer

$$8 \ \mathrm{kg}$$

Question 7

Two kids ($$m_1 = 50$$ \ \mathrm{kg}$$, m_2$ = 40 \ \mathrm{kg}) $$sit at the ends of a $$5 \ \mathrm{m}$$, $$30 \ \mathrm{kg}$$ seesaw. How far from the left end should the fulcrum be placed for equilibrium?

Accepted Answer

$$2.8 \ \mathrm{m}$$

Question 8

A uniform board $$6 \ \mathrm{m}$$ long, $$12 \ \mathrm{kg}$$, is held by two ropes at its ends. An $$8 \ \mathrm{kg}$$ object is placed $$1 \ \mathrm{m}$$ from the left end. What is the tension in the left rope?

Accepted Answer

$$70 \ \mathrm{N}$$

Question 9

A $$70 \ \mathrm{kg}$$, $$1.9 \ \mathrm{m}$$ man does push-ups at $$20^\circ to $$the floor. His feet are $$1.15 \ \mathrm{m}$$ below and his arms $$0.4 \ \mathrm{m}$$ above his center of mass. What is the force on each hand from the floor? (Assume $$g = 10 \ \mathrm{m/s^2$})$$

Accepted Answer

$$525 \ \mathrm{N}$$

Question 10

A ladder of mass $$10 \ \mathrm{kg}$$ and length $$4 \ \mathrm{m}$$ rests against a wall at $$53^\circ$$ with the horizontal. What is the minimum coefficient of static friction $$\mu_s$$ required to prevent slipping?

Accepted Answer

$$\mu_s = \dfrac{1}{4}$$

Question 11

A $$50 \ \mathrm{kg}$$ girl climbs $$2 \ \mathrm{m} up a$$ $$6 \ \mathrm{m}$$, $$20 \ \mathrm{kg}$$ ladder leaning at $$60^\circ$$ with the horizontal. What is the total contact force at the bottom of the ladder?

Accepted Answer

$$800 \ \mathrm{N}$$

Question 12

A $$300 \ \mathrm{kg}$$, $$4 \ \mathrm{m}$$ beam is held horizontally by a hinge and a cable making $$37^\circ$$ with the horizontal. What is the magnitude of the tension in the cable?

Accepted Answer

$$2400 \ \mathrm{N}$$

Question 13

A $$400 \ \mathrm{kg}$$, $$8 \ \mathrm{m}$$ beam is held horizontally by a hinge and a cable at $$53^\circ$$ with the horizontal, with a $$500 \ \mathrm{kg}$$ mass hanging from the right edge. What is the net force the hinge applies to the beam?

Accepted Answer

$$13000 \ \mathrm{N}$$

Question 14

A $$200 \ \mathrm{kg}$$, $$4 \ \mathrm{m}$$ beam is held by a hinge and a cable at $$53^\circ$$ with the wall. A $$100 \ \mathrm{kg}$$ mass hangs from the end. What is the angle the net force from the hinge makes with the horizontal?

Accepted Answer

$$+53^\circ$$

Question 15

A $$100 \ \mathrm{kg}$$, $$4 \ \mathrm{m}$$ beam is held at $$30^\circ$$ above the horizontal by a hinge and a force applied at its edge at $$50^\circ$$ above the horizontal. What is the magnitude of the force you must apply?

Accepted Answer

$$250 \ \mathrm{N}$$

Question 16

A $$200 \ \mathrm{kg}$$, $$10 \ \mathrm{m}$$ beam is held at $$53^\circ$$ above the horizontal by a hinge and a rope at $$30^\circ$$ with the beam. What is the angle the net force from the hinge makes with the horizontal?

Accepted Answer

$$-30^\circ$$

Question 17

When solving equilibrium problems, why is it advantageous to choose the axis of rotation at a point where multiple unknown forces act?

Accepted Answer

Because it allows you to ignore the torques from those unknown forces.

Question 18

For a rigid body with uniform mass distribution, where does its weight act?

Accepted Answer

At the geometric center of the body.

Question 19

A $$80 \ \mathrm{kg}$$, $$2 \ \mathrm{m}$$ man lies horizontally on a $$2 \ \mathrm{m}$$ board. The left and right scales read $$320 \ \mathrm{N}$$ and $$480 \ \mathrm{N}$$, respectively. How far from the man's head is his center of mass? (Assume $$g = 10 \ \mathrm{m/s^2$})$$

Accepted Answer

$$1.2 \ \mathrm{m}$$

Static Equilibrium and Rigid Body Mechanics: Study Notes

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