Download Review Questions

Review Questions
Mark the following statements true or false. If you mark it false, tell why it is false and
how it could be changed to make it true.
1. If a force F acts on a particle of mass m which is moving at a speed v, we define
the work done to be the change in the quantity 1/2mv^2. NO: this is only the
kinetic energy change, but there is also the potential energy to be taken into
account. Work changes the total energy which is the sum of BOTH the kinetic
energy and the potential energy
2. Work is necessarily a positive quantity. NO: it has the sign of the scalar product
of the force and the displacement, which can be negative, zero, and positive.
3. The definition of work as force times distance moved is generally valid only for
one-dimensional problems. YES
4. The dimensions of work are the same as those of energy. YES
5. Joule, foot-pound, watt-second, and erg are all units of energy.YES
6. If several forces act on a particle, the total work done by all of them is the work
done by the net resultant force.YES
7. The theorem stating that the net work done on a particle is equal to its change of
kinetic energy is generally valid only for one-dimensional problems. NO: one
dimensional particles can have potential energy too (springs, electric fields, etc).
If the theorem wants to say only kinetic energy, it must specify that there are no
other forces acting on the particle.
8. In the most general case, the work-energy theorem states that the net work done,
over and interval, by the resultant force on a particle is equal to the change in the
particle’s kinetic energy. YES – this is only for the RESULTANT force which is
the sum of all forces acting on the particle
9. An object, starting from rest, slides down a frictionless hill; its speed at the
bottom depends only on the height, and not the shape of the hill. YES
10. The work done on an object by frictional forces is always negative. NO: imagine
a case of an object on a frictionless surface accelerated by friction between the
object and your hand or another object – then the work done by the friction is
positive.
11. A heavy crate is dragged across a rough floor from point A to point B; the work
done on it is independent of the path taken from A to B. NO: the work is done to
overcome the friction and so it is proportional to the length of the path.
12. A heavy crate is dragged across a rough floor from point A to point B; the work
done by the normal force of the floor on the crate is independent of the path taken
from A to B. YES: the work done by the normal force is just zero.
13. If a 50-lb box is lifted, slowly and steadily, 4ft above the floor, the work done on
the box is 200 ft-lb. YES
14. If a 50-lb box is lifted, slowly and steadily, 4ft above the floor, the box’s kinetic
energy is increased by 200 ft-lb. NO: all the work goes in this case in the potential
energy
15. If a 50-lb box is lifted, slowly and steadily, 4ft above the floor, the box’s potential
energy is increased by 200 ft-lb. YES
16. If a 50-lb box is lifted, slowly and steadily, 4ft above the floor, the work done on
the box by gravity is -200ft-lb.YES
17. A block slides down an incline; conservation principles say that the work done on
the block by the incline is equal to the work done on the incline by the block. NO:
if the incline does not move in the frame of reference taken (which is usually the
case) the work done on the incline is zero, whereas the work of friction between
the incline and the body is not zero (negative). Conservations principles say: (the
work done on the block by the incline) = - (the thermal energy produced by
heating of both the incline and the block).
18. The following units all measure the same physical quantity: foot-pound/second,
horsepower, watt, joule. NO: the first three do indeed measure the same quantity
which is power, but Joule measures energy.
19. Potential energy can be regarded as work that is “stored” by being done against
some force.YES
20. Potential energy and work have the same dimensions. YES
21. Potential energy can be unambiguously associated only with a conservative force.
YES
22. If a body is acted upon only by conservative forces, the sum of its potential and
kinetic energy is constant. YES
23. A conservative force is one such that the work it does on a particle in moving it
along any path is zero. NO: the work done along a path is zero for any closed path
(that is a path that ends at the same point it starts). Otherwise, the work can be
zero or non-zero
24. Friction is a non-conservative force. YES
25. If a particle is acted upon only by conservative forces, then whenever it returns to
its initial position, it has its initial velocity. YES
26. In one dimension, any force which depends only on the position of the particle is
conservative. YES
27. The work done by a conservative force on a particle is equal to the increase of the
corresponding potential energy of the particle. NO: the sign is wrong; the correct
statement is: (The work done by a conservative force on a particle) = -(the
increase of the corresponding potential energy of the particle)
28. The absolute value of potential energy is indeterminate. YES
29. A force is non conservative if the work done by it in moving a particle between
two given points depends on the path taken. YES
30. The force of Earth’s gravity does positive work on any satellite in a circular orbit
around the earth. NO: if the orbit is circular, and we neglect the deviations of the
planet from a perfect sphere, the said work is zero, because the force is always
perpendicular to the velocity.
31. As a simple pendulum swings back and forth, the tension in the supporting cord
does work on the pendulum. NO: the work done by the tension is always zero
because the tension is always perpendicular to the velocity.
32. The total mechanical energy of an object is conserved if the net force on the body
is zero. NO: only the kinetic energy is conserved: consider a body being dragged
up a hill with a constant speed: its acceleration is zero, so the sum of all forces is
zero, however its total mechanical energy is equal its potential energy which
grows up.
33. The work done on a system by non-conservative forces is equal to the change in
its total mechanical energy. YES, if all the possible conservative forces are
classified as mechanical (i.e. gravity, electrostatic, etc)