Q: Consider a block sliding up an incline with friction. If the block starts from rest and is pulled a distance $$d up $$the incline, which of the following expressions gives the minimum tension $$T$$ required in the rope to move the block at constant speed?

$$T = M g \sin\theta + \mu_k M g \cos\theta$$

Question 1

A block of mass $$M is $$pulled up an inclined plane at angle $$	heta by a $$tension $$T in a $$rope passing over a frictionless pulley. The coefficient of kinetic friction between the block and the plane is $$\mu_k. $$Which of the following correctly expresses the work done by friction as the block moves a distance $$d up $$the incline?

Accepted Answer

Question 2

When analyzing the energy changes as a block is pulled up an incline with friction, which of the following correctly represents the change in mechanical energy $$\Delta E of $$the block?

Accepted Answer

$$\Delta E = W_{T} + W_{fric}$$

Question 3

A block of mass $$M is $$pulled up an incline at constant speed. Which of the following statements is true about the net work done on the block?

Accepted Answer

The net work done is zero because the block's kinetic energy does not change.

Question 4

Consider a block sliding up an incline with friction. If the block starts from rest and is pulled a distance $$d up $$the incline, which of the following expressions gives the minimum tension $$T$$ required in the rope to move the block at constant speed?

Accepted Answer

$$T = M g \sin	heta + \mu_k M g \cos	heta$$

Question 5

A block is moved along a path from point $$A to$$ $$B$$ horizontally, then from $$B to$$ $$C$$ vertically, and finally from $$C to$$ $$D$$ horizontally back to the starting height. If only gravity acts, what is the total work done by gravity over the entire path?

Accepted Answer

$$W_{g} = mgh$$

Question 6

If a block is moved in a closed path in a uniform gravitational field, what can be said about the work done by gravity?

Accepted Answer

The work done by gravity is zero for any closed path.

Question 7

A block is moved from point $$A to$$ $$B$$ along two different paths in the presence of friction. Which statement is correct about the work done by friction?

Accepted Answer

The work done by friction depends on the path taken.

Question 8

Which of the following is a defining property of a conservative force?

Accepted Answer

The work done by the force is independent of the path taken.

Question 9

A steam locomotive generates power by injecting steam into a piston. If the locomotive must pull a train up a $$2.5\%$$ grade at constant speed, which of the following best describes the minimum power required?

Accepted Answer

$$P = F_{total} v$$

Question 10

If a train of mass $$m$$ moves at constant speed $$v up a $$grade of $$	heta$$, what is the expression for the power required to overcome gravity alone?

Accepted Answer

$$P = m g v \sin	heta$$

Question 11

A block is pulled up an incline at constant speed. Which of the following is true about the forces acting on the block?

Accepted Answer

The sum of the tension, friction, and gravity components parallel to the incline is zero.

Question 12

Which of the following correctly expresses the work done by gravity when a block of mass $$m is $$lifted vertically a height $$h$$?

Accepted Answer

$$W_g = -mgh$$

Question 13

If a block is moved from point $$A to$$ $$B$$ along a path with friction, and then back to $$A$$ along a different path, what is the total work done by friction?

Accepted Answer

The total work done by friction is negative and depends on the total distance traveled.

Question 14

A steam locomotive has a maximum power output $$P_{max}. If $$the train moves at speed $$v$$ and the total resistive force is $$F_{res}$$, which of the following limits the maximum speed the train can achieve?

Accepted Answer

$$v_{max} = \frac{P_{max}}{F_{res}}$$

Question 15

Which of the following statements is true about the work done by a non-conservative force such as friction?

Accepted Answer

It depends on the path taken between two points.

Question 16

A block is moved in a square path in the presence of gravity. What is the net work done by gravity after one complete loop?

Accepted Answer

$$W_g = 0$$

Question 17

If a block is moved vertically upward by a distance $$h$$ and then horizontally by a distance $$d$$, what is the total work done by gravity?

Accepted Answer

$$W_g = -mgh$$

Question 18

A train moves at constant speed up a $$2.5\%$$ grade. If the resistive force is $$F_{res}$$ and the train's speed is $$v$$, what is the power required to maintain this motion?

Accepted Answer

$$P = F_{res} v$$

Work, Energy, and Forces: Physics 407 Homework Study Notes

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