A 2.0-kg block slides down a frictionless incline from point A to point B. A force (magnitude P = 3.0 N) acts on the block between A and B, as shown. Points A and B are 2.0 m apart. If the kinetic energy of the block at A is 10 J, what is the kinetic energy of the block at B?
![](data:image/png;base64,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)
a.
27 J
b.
20 J
c.
24 J
d.
17 J
e.
37 J
[Ques. 2] A block slides on a rough horizontal surface from point A to point B. A force (magnitude P = 2.0 N) acts on the block between A and B, as shown. Points A and B are 1.5 m apart. If the kinetic energies of the block at A and B are 5.0 J and 4.0 J, respectively, how much work is done on the block by the force of friction as the block moves from A to B?
![](data:image/png;base64,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)
a.
3.3 J
b.
+1.3 J
c.
+3.3 J
d.
1.3 J
e.
+4.6 J
[Ques. 3] A 4.0-kg block is lowered down a 37 incline a distance of 5.0 m from point A to point B. A horizontal force (F = 10 N) is applied to the block between A and B as shown in the figure. The kinetic energy of the block at A is 10 J and at B it is 20 J. How much work is done on the block by the force of friction between A and B?
![](data:image/png;base64,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)
a.
58 J
b.
53 J
c.
68 J
d.
63 J
e.
47 J
[Ques. 4] A force acting on an object moving along the
x axis is given by
Fx = (14
x 3.0
x2) N where
x is in m. How much work is done by this force as the object moves from
x = 1 m to
x = +2 m?
a.
+12 J
b.
+28 J
c.
+40 J
d.
+42 J
e.
28 J
[Ques. 5] A body moving along the
x axis is acted upon by a force
Fx that varies with
x as shown. How much work is done by this force as the object moves from
x = 1 m to
x = 8 m?
a.
2 J
b.
18 J
c.
10 J
d.
26 J
e.
+18 J
[Ques. 6] An object moving along the
x axis is acted upon by a force
Fx that varies with position as shown. How much work is done by this force as the object moves from
x = 2 m to
x = 8 m?
a.
10 J
b.
+10 J
c.
+30 J
d.
30 J
e.
+40 J
[Ques. 7] A block is pushed across a rough horizontal surface from point A to point B by a force (magnitude P = 5.4 N) as shown in the figure. The magnitude of the force of friction acting on the block between A and B is 1.2 N and points A and B are 0.5 m apart. If the kinetic energies of the block at A and B are 4.0 J and 5.6 J, respectively, how much work is done on the block by the force P between A and B?
![](data:image/png;base64,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)
a.
2.7 J
b.
1.0 J
c.
2.2 J
d.
1.6 J
e.
3.2 J
[Ques. 8] The two masses in the figure are released from rest. After the 3.0-kg mass has fallen 1.5 m, it is moving with a speed of 3.8 m/s. What is the change in mechanical energy done on the system during this time interval by the frictional force on the 2.0 kg mass?
![](data:image/png;base64,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<!--MESSAGE)