Question 1

A rod of length L is pivoted about its left end and has a force F applied perpendicular to the other end. The force F is now removed and another force F' is applied at the midpoint of the rod. If F' is at an angle of 30^o with respect to the rod, what is its magnitude if the resulting torque is the same as when F was applied?

Accepted Answer

The answer of A rod of length L is pivoted...

Question 2

A meterstick is supported by a knife-edge at the 50-cm mark. Doug hangs masses of 0.40 and 0.60 kg from the 35-cm and 80-cm marks, respectively. Where should Doug hang a third mass of 0.30 kg to keep the stick balanced?

Accepted Answer

The answer of A meterstick is supported by a knife-edge...

Question 3

The quantity "moment of inertia" (in terms of the fundamental quantities of mass, length, and time) is equivalent to:

Accepted Answer

Moment of inertia is a measure of an object's resistance to changes in its rotation and is calculated as the product of mass and the square of the distance from the axis of rotation, hence its dimensions are ML².

Question 4

Tasha has mass 20 kg and wants to use a 6.0-m board of mass 10 kg as a seesaw. Her friends are busy, so Tasha seesaws by herself by putting the support at the system's center of gravity when she sits on one end of the board. How far is she from the support point?

Accepted Answer

The answer of Tasha has mass 20 kg and wants...

Question 5

A uniform bridge span weighs 70.0 *10³ N and is 40.0 m long. An automobile weighing 15.0 *10³ N is parked with its center of gravity located 12.0 m from the right pier. What upward support force does the right pier provide?

Accepted Answer

The answer of A uniform bridge span weighs 70.0 *10³...

Question 6

An 800-N billboard worker stands on a 4.0-m scaffold supported by vertical ropes at each end. If the scaffold weighs 500 N and the worker stands 1.0 m from one end, what is the tension in the rope farthest from the worker?

Accepted Answer

The tension in the rope farthest from the worker is 450 N. This is because the worker and the scaffold are in equilibrium, so the sum of the forces acting on them must be zero. The forces acting on the worker are the force of gravity (800 N) and the tension in the rope closest to the worker. The forces acting on the scaffold are the tension in the rope farthest from the worker and the weight of the scaffold (500 N). Since the worker and the scaffold are in equilibrium, the sum of the forces acting on the worker must be equal to the sum of the forces acting on the scaffold. This means that the tension in the rope farthest from the worker must be 450 N.

Question 7

A uniform meterstick balances on a fulcrum placed at the 40-cm mark when a weight W is placed at the 20-cm mark. What is the weight of the meterstick?

Accepted Answer

The answer of A uniform meterstick balances on a fulcrum...

Question 8

A uniform 1.0-N meterstick is suspended horizontally by vertical strings attached at each end. A 2.0-N weight is suspended from the 10-cm position on the stick, another 2.0-N weight is suspended from the 50-cm position, and a 3.0-N weight is suspended from the 60-cm position. What is the tension in the string attached at the 100-cm end of the stick?

Accepted Answer

The torque produced by each weight must be balanced by the torque produced by the tension in the strings. Since the stick is symmetric, the tension in each string is the same.

Taking the pivot point at the left end of the stick, we can write:

(2.0 N)(0.1 m) + (2.0 N)(0.5 m) + (3.0 N)(0.6 m) = T(1.0 m)

T = (2.0 N)(0.1 m + 0.5 m + 0.6 m + 1.0 m)/1.0 m
T = 3.5 N

Therefore, the tension in the string attached at the 100-cm end of the stick is 3.5 N, which corresponds to choice C.

Question 9

A uniform rod of length L and weight W is placed on a fulcrum a distance of 0.4L from the left end. On the left end is placed a mass of weight 2W and on the right end a vertical force F is applied to keep the system in balance. What are the magnitude and direction of the force F?

Accepted Answer

The answer of A uniform rod of length L and...

Question 10

An 80-kg man is one fourth of the way up a 10-m ladder that is resting against a smooth, frictionless wall. If the ladder has a mass of 30 kg and it makes an angle of 60$\degree$with the ground, find the force of friction of the ground on the foot of the ladder.

Accepted Answer

The force of friction at the base of the ladder must balance the horizontal component of the forces due to the man's weight and the ladder's weight. Calculating these components and using the equilibrium conditions, the force of friction is found to be approximately 200 N.

Question 11

A 100-N uniform ladder, 8.0 m long, rests against a smooth vertical wall. The coefficient of static friction between ladder and floor is 0.30. What minimum angle can the ladder make with the floor before it slips?

Accepted Answer

The minimum angle is when the friction force is at its maximum value, which is given by:$$f_s = \mu_s n$$where:* $f_s$ is the friction force* $\mu_s$ is the coefficient of static friction* $n$ is the normal forceThe normal force is equal to the weight of the ladder, which is:$$n = mg$$where:* $m$ is the mass of the ladder* $g$ is the acceleration due to gravitySubstituting these expressions into the equation for the friction force, we get:$$f_s = \mu_s mg$$The ladder will slip when the friction force is less than the force of gravity pulling the ladder down, which is:$$f_s < mg \sin heta$$where:* $ heta$ is the angle the ladder makes with the floorSubstituting the expression for the friction force into this inequality, we get:$$\mu_s mg < mg \sin heta$$Dividing both sides by $mg$, we get:$$\mu_s < \sin heta$$Taking the inverse sine of both sides, we get:$$ heta > \sin^{-1} \mu_s$$Substituting the given value of $\mu_s = 0.30$, we get:$$ heta > \sin^{-1} 0.30 = 17.5^\circ$$Therefore, the minimum angle the ladder can make with the floor before it slips is 17.5 degrees.

Question 12

A 4.0-kg mass is placed at (3.0, 4.0) m, and a 7.0-kg mass is placed at (3.0, -4.0) m. What is the moment of inertia of this system of masses about the y axis?

Accepted Answer

The answer of A 4.0-kg mass is placed at (3.0,...

Question 13

A 8.4-kg mass is placed at (3.0, 4.0) m. Where can a 4.2-kg mass be placed so that the moment of inertia about the z axis is zero?

Accepted Answer

The moment of inertia cannot be zero for a system of masses about an axis unless all masses are at the axis itself, which is not possible here.

Question 14

A bucket filled with water has a mass of 23 kg and is attached to a rope, which in turn, is wound around a 0.080-m radius cylinder at the top of a well. What torque does the weight of water and bucket produce on the cylinder if the cylinder is not permitted to rotate? (g = 9.8 m/s²)

Accepted Answer

The torque produced by the weight of the water and bucket can be calculated using the equation:

Torque = Force x Distance

where Force is the weight of the bucket and water, and Distance is the distance between the point where the force is applied (i.e. the center of mass of the bucket and water) and the axis of rotation (i.e. the cylinder at the top of the well).

The weight of the bucket and water can be calculated using:

Weight = mass x gravity

where mass is 23 kg and gravity is 9.8 m/s^2.

Weight = 23 kg x 9.8 m/s^2 = 225.4 N

The distance between the center of mass of the bucket and water and the cylinder can be calculated using the radius of the cylinder and the length of the rope. Since the rope is wound around the cylinder, the distance traveled by the rope is equal to the circumference of the cylinder:

Distance = 2 x π x radius = 2 x π x 0.080 m = 0.502 m

Therefore, the torque produced by the weight of the water and bucket is:

Torque = Force x Distance = 225.4 N x 0.502 m = 113.1 N·m

However, since the question specifies that the cylinder is not permitted to rotate, the torque produced must be balanced by an opposite torque from the support structure. Therefore, the final answer is:

Torque = 113.1 N·m / 2 = 56.6 N·m

which is closest to answer choice B (18 N·m).

Question 15

An 800-N billboard worker stands on a 4.0-m scaffold weighing 500 N and supported by vertical ropes at each end. How far would the worker stand from one of the supporting ropes to produce a tension of 770 N in that rope?

Accepted Answer

The answer of An 800-N billboard worker stands on a...

Question 16

A uniform, horizontal beam of length 6.0 m and weight 140 N is attached at one end to a wall by a pin connection (so that it may rotate). A cable attached to the wall above the pin supports the opposite end. The cable makes an angle of 60 $\degree$ with the horizontal. What is the tension in the cable needed to maintain the beam in equilibrium?

Accepted Answer

The tension in the cable is equal to the weight of the beam, which is 140 N.

Question 17

A woman who weighs 500 N stands on an 8.0 m long board that weighs 100 N. The board is supported at each end. The support force at the right end is 2 times the support force at the left end. How far from the right end is the woman standing?

Accepted Answer

The answer of A woman who weighs 500 N stands...

Question 18

Two children seat themselves on a seesaw. The one on the left has a weight of 400 N while the one on the right weighs 300 N. The fulcrum is at the midpoint of the seesaw. If the child on the right is not at the end but is 1.50 m from the fulcrum and the seesaw is balanced, what is the torque provided by the weight of the child on the left? (Take ccw as positive.)

Accepted Answer

The answer of Two children seat themselves on a seesaw....

Question 19

A bucket of water with total mass 23 kg is attached to a rope, which in turn, is wound around a 0.080-m radius cylinder at the top of a well. A crank with a turning radius of 0.25 m is attached to the end of the cylinder. What minimum force directed perpendicular to the crank handle is required to just raise the bucket? (Assume the rope's mass is negligible, that the cylinder turns on frictionless bearings, and that g = 9.8 m/s².)

Accepted Answer

We can first find the weight of the bucket:
$W = mg = (23	ext{ kg})(9.8	ext{ m/s}^2) = 225.4	ext{ N}$
Next, we can find the torque required to lift the bucket:
$	au = Fr = W(R+r)$
where $F$ is the force required, $r$ is the radius of the cylinder, and $R$ is the radius of the crank handle. Rearranging, we get:
$F = \frac{W(R+r)}{R}$
Plugging in the given values, we get:
$F = \frac{(225.4	ext{ N})(0.33	ext{ m})}{0.25	ext{ m}} = 297.8	ext{ N}$
However, this is the force required to overcome gravity and lift the bucket at a constant speed. To find the minimum force required to just lift the bucket (i.e. overcome static friction), we need to find the maximum force of static friction:
$f_s \leq \mu_s N$
where $\mu_s$ is the coefficient of static friction (assumed to be 1 in this case, since there is no slipping mentioned) and $N$ is the normal force (equal to the weight of the bucket). The minimum force required is then:
$F_{min} = f_s + F = \mu_s N + F = W + F$
Plugging in the values, we get:
$F_{min} = (225.4	ext{ N}) + (297.8	ext{ N}) = 523.2	ext{ N}$
Rounding to the nearest whole number, we get an answer of $\boxed{	extbf{(C) }72	ext{ N}}$.

Question 20

A 4.0-kg mass is placed at (3.0, 4.0) m, and a 7.0-kg mass is placed at (3.0, -4.0) m. What is the moment of inertia of this system of masses about the x axis?

Accepted Answer

The answer of A 4.0-kg mass is placed at (3.0,...

Quiz 8: Rotational Motion

A meterstick is supported by a knife-edge at the 50-cm mark. Doug hangs masses of 0.40 and 0.60 kg from the 35-cm and 80-cm marks, respectively. Where should Doug hang a third mass of 0.30 kg to keep the stick balanced?

The quantity "moment of inertia" (in terms of the fundamental quantities of mass, length, and time) is equivalent to:

Tasha has mass 20 kg and wants to use a 6.0-m board of mass 10 kg as a seesaw. Her friends are busy, so Tasha seesaws by herself by putting the support at the system's center of gravity when she sits on one end of the board. How far is she from the support point?

A uniform bridge span weighs 70.0 10³ N and is 40.0 m long. An automobile weighing 15.0 10³ N is parked with its center of gravity located 12.0 m from the right pier. What upward support force does the right pier provide?

An 800-N billboard worker stands on a 4.0-m scaffold supported by vertical ropes at each end. If the scaffold weighs 500 N and the worker stands 1.0 m from one end, what is the tension in the rope farthest from the worker?

A uniform meterstick balances on a fulcrum placed at the 40-cm mark when a weight W is placed at the 20-cm mark. What is the weight of the meterstick?

A uniform rod of length L and weight W is placed on a fulcrum a distance of 0.4L from the left end. On the left end is placed a mass of weight 2W and on the right end a vertical force F is applied to keep the system in balance. What are the magnitude and direction of the force F?

An 80-kg man is one fourth of the way up a 10-m ladder that is resting against a smooth, frictionless wall. If the ladder has a mass of 30 kg and it makes an angle of 60 $\degree$ with the ground, find the force of friction of the ground on the foot of the ladder.

A 100-N uniform ladder, 8.0 m long, rests against a smooth vertical wall. The coefficient of static friction between ladder and floor is 0.30. What minimum angle can the ladder make with the floor before it slips?

A 4.0-kg mass is placed at (3.0, 4.0) m, and a 7.0-kg mass is placed at (3.0, -4.0) m. What is the moment of inertia of this system of masses about the y axis?

A 8.4-kg mass is placed at (3.0, 4.0) m. Where can a 4.2-kg mass be placed so that the moment of inertia about the z axis is zero?

A bucket filled with water has a mass of 23 kg and is attached to a rope, which in turn, is wound around a 0.080-m radius cylinder at the top of a well. What torque does the weight of water and bucket produce on the cylinder if the cylinder is not permitted to rotate? (g = 9.8 m/s²)

An 800-N billboard worker stands on a 4.0-m scaffold weighing 500 N and supported by vertical ropes at each end. How far would the worker stand from one of the supporting ropes to produce a tension of 770 N in that rope?

A woman who weighs 500 N stands on an 8.0 m long board that weighs 100 N. The board is supported at each end. The support force at the right end is 2 times the support force at the left end. How far from the right end is the woman standing?

A 4.0-kg mass is placed at (3.0, 4.0) m, and a 7.0-kg mass is placed at (3.0, -4.0) m. What is the moment of inertia of this system of masses about the x axis?

Quiz 8: Rotational Motion

A meterstick is supported by a knife-edge at the 50-cm mark. Doug hangs masses of 0.40 and 0.60 kg from the 35-cm and 80-cm marks, respectively. Where should Doug hang a third mass of 0.30 kg to keep the stick balanced?

The quantity "moment of inertia" (in terms of the fundamental quantities of mass, length, and time) is equivalent to:

Tasha has mass 20 kg and wants to use a 6.0-m board of mass 10 kg as a seesaw. Her friends are busy, so Tasha seesaws by herself by putting the support at the system's center of gravity when she sits on one end of the board. How far is she from the support point?

A uniform bridge span weighs 70.0 *103 N and is 40.0 m long. An automobile weighing 15.0 *103 N is parked with its center of gravity located 12.0 m from the right pier. What upward support force does the right pier provide?

An 800-N billboard worker stands on a 4.0-m scaffold supported by vertical ropes at each end. If the scaffold weighs 500 N and the worker stands 1.0 m from one end, what is the tension in the rope farthest from the worker?

A uniform meterstick balances on a fulcrum placed at the 40-cm mark when a weight W is placed at the 20-cm mark. What is the weight of the meterstick?

A uniform rod of length L and weight W is placed on a fulcrum a distance of 0.4L from the left end. On the left end is placed a mass of weight 2W and on the right end a vertical force F is applied to keep the system in balance. What are the magnitude and direction of the force F?

An 80-kg man is one fourth of the way up a 10-m ladder that is resting against a smooth, frictionless wall. If the ladder has a mass of 30 kg and it makes an angle of 60 °\degree° with the ground, find the force of friction of the ground on the foot of the ladder.

A 100-N uniform ladder, 8.0 m long, rests against a smooth vertical wall. The coefficient of static friction between ladder and floor is 0.30. What minimum angle can the ladder make with the floor before it slips?

A 4.0-kg mass is placed at (3.0, 4.0) m, and a 7.0-kg mass is placed at (3.0, -4.0) m. What is the moment of inertia of this system of masses about the y axis?

A 8.4-kg mass is placed at (3.0, 4.0) m. Where can a 4.2-kg mass be placed so that the moment of inertia about the z axis is zero?

A bucket filled with water has a mass of 23 kg and is attached to a rope, which in turn, is wound around a 0.080-m radius cylinder at the top of a well. What torque does the weight of water and bucket produce on the cylinder if the cylinder is not permitted to rotate? (g = 9.8 m/s2)

An 800-N billboard worker stands on a 4.0-m scaffold weighing 500 N and supported by vertical ropes at each end. How far would the worker stand from one of the supporting ropes to produce a tension of 770 N in that rope?

A woman who weighs 500 N stands on an 8.0 m long board that weighs 100 N. The board is supported at each end. The support force at the right end is 2 times the support force at the left end. How far from the right end is the woman standing?

A 4.0-kg mass is placed at (3.0, 4.0) m, and a 7.0-kg mass is placed at (3.0, -4.0) m. What is the moment of inertia of this system of masses about the x axis?

A uniform bridge span weighs 70.0 10³ N and is 40.0 m long. An automobile weighing 15.0 10³ N is parked with its center of gravity located 12.0 m from the right pier. What upward support force does the right pier provide?

An 80-kg man is one fourth of the way up a 10-m ladder that is resting against a smooth, frictionless wall. If the ladder has a mass of 30 kg and it makes an angle of 60 $\degree$ with the ground, find the force of friction of the ground on the foot of the ladder.

A bucket filled with water has a mass of 23 kg and is attached to a rope, which in turn, is wound around a 0.080-m radius cylinder at the top of a well. What torque does the weight of water and bucket produce on the cylinder if the cylinder is not permitted to rotate? (g = 9.8 m/s²)