Q: A mechanic uses a 0.80 m long wrench and applies a force of 900 N at an angle of $$19^\circ to $$the wrench. What is the magnitude of the torque about the bolt?

$$\tau = 900 \times 0.80 \times \sin(19^\circ) = 234 \ \mathrm{N \cdot m}$$

Q: A uniform bar of length $$L = 0.50 m $$and mass $$0.10 kg $$has a $$0.08 kg $$mass glued to its left end and a $$0.10 kg $$mass glued to its right end. Where is the center of gravity measured from the left end?

$$x_{cg} = \frac{0.08 \times 0 + 0.10 \times 0.50 + 0.10 \times 0.50}{0.08 + 0.10 + 0.10} = 0.24 m$$

Q: Which of the following is the correct vector expression for torque $$\vec{\tau}$$ produced by a force $$\vec{F}$$ applied at position $$\vec{r}$$ relative to point $$O$$?

$$\vec{\tau} = \vec{r} \times \vec{F}$$

Question 1

A force $$\vec{F} is $$applied at a distance $$r$$ from the axis of rotation, making an angle $$	heta$$ with the position vector $$\vec{r}. $$What is the correct formula for the magnitude of the torque $$	au$$ produced by this force about the axis?

Accepted Answer

$$	au = rF\sin	heta$$

Question 2

Which of the following statements about static equilibrium is correct?

Accepted Answer

Both the sum of all external forces and the sum of all external torques must be zero.

Question 3

A mechanic uses a 0.80 m long wrench and applies a force of 900 N at an angle of $$19^\circ to $$the wrench. What is the magnitude of the torque about the bolt?

Accepted Answer

$$	au = 900 	imes 0.80 	imes \sin(19^\circ) = 234 \ \mathrm{N \cdot m}$$

Question 4

A force $$\vec{F}$$ acts along the line passing through the axis of rotation $$O. $$What is the torque produced by this force about $$O$$?

Accepted Answer

The torque is zero.

Question 5

A uniform bar of length $$L = 0.50 m $$and mass $$0.10 kg $$has a $$0.08 kg $$mass glued to its left end and a $$0.10 kg $$mass glued to its right end. Where is the center of gravity measured from the left end?

Accepted Answer

$$x_{cg} = \frac{0.08 	imes 0 + 0.10 	imes 0.50 + 0.10 	imes 0.50}{0.08 + 0.10 + 0.10} = 0.24 m$$

Question 6

A car is parked on a slope. Under what condition will the car remain in equilibrium?

Accepted Answer

The center of gravity must be directly above the area of support.

Question 7

A man of mass $$75 kg $$pauses in a push-up position with his center of gravity $$40 cm $$from his hands and $$95 cm $$from his feet. What is the normal force exerted by the floor on each hand?

Accepted Answer

$$F_{	ext{hand}} = 259 N$$

Question 8

Which of the following best describes the role of the biceps muscle in the human arm?

Accepted Answer

It acts as a flexor to bend the arm.

Question 9

A person holds a 4.0 kg book in their hand with the forearm horizontal. The biceps attaches 4.0 cm from the elbow, the center of gravity of the forearm is 16 cm from the elbow, and the book is 38 cm from the elbow. What is the main reason the force exerted by the biceps is much greater than the weight of the book and forearm?

Accepted Answer

The biceps attaches close to the elbow, creating a small lever arm.

Question 10

A uniform beam of length $$L = 2.10 m $$and mass $$m = 6.50 kg $$supports a $$25.0 kg $$crate at its end. A wire makes an angle $$	heta = 30^\circ$$ with the beam and is attached at the midpoint. What is the tension $$T in $$the wire?

Accepted Answer

$$T = 640 N$$

Question 11

Which of the following is the correct vector expression for torque $$\vec{	au}$$ produced by a force $$\vec{F}$$ applied at position $$\vec{r}$$ relative to point $$O$$?

Accepted Answer

$$\vec{	au} = \vec{r} 	imes \vec{F}$$

Question 12

A force $$F is $$applied perpendicular to a wrench at a distance $$r$$ from the pivot. What is the torque produced?

Accepted Answer

$$	au = Fr$$

Question 13

If a force is applied at an angle to the lever arm, which component of the force produces torque?

Accepted Answer

The component perpendicular to the lever arm.

Question 14

A beam is in static equilibrium. Which of the following must be true?

Accepted Answer

The sum of all torques about any point is zero.

Question 15

A person bends forward, and the erector spinae muscles exert a force to keep the upper body horizontal. If the total weight of the upper body is $$w$$, and the force of the back muscles is $$F_M$$, which of the following is true about the torque equilibrium about the fifth lumbar vertebra?

Accepted Answer

The sum of the torques due to $$w$$ and $$F_M$$ must be zero.

Question 16

A beam is supported at one end by a hinge and at the other by a wire at angle $$	heta. If $$the wire breaks, what happens to the beam?

Accepted Answer

It rotates downward about the hinge.

Question 17

Which of the following best describes the effect of increasing the lever arm while keeping the force constant?

Accepted Answer

The torque increases.

Question 18

A force is applied at the pivot point of a lever. What is the resulting torque?

Accepted Answer

Zero torque.

Question 19

A uniform beam is in equilibrium, supported at both ends. If a heavy object is placed near one end, what must happen to the support forces?

Accepted Answer

The support force at the near end increases, and at the far end decreases.

Statics and Torque: Principles and Applications

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