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Work and Energy (1)
White Board Practice
1. The graph to the right represents the potential energy U
as a function of position r for a particle of mass m. If the
particle is released from rest at position ro, what will its
speed be at position 3ro?
8𝑈𝑜
𝑚
a. √
Justify your answer
4𝑈𝑜
𝑚
b. √
2𝑈𝑜
𝑚
c. √
6𝑈𝑜
𝑚
d. √
2. A small particle slides along a track with elevated ends and a flat central part. The flat part has a length L = 2.0 m. the
curved portions of the track are frictionless. For the flat part, the coefficient of kinetic friction is μk = 0.20. the particle is
released at point A which is a height h = 1.0 m above the flat part of the track. At what height does the particle reach in
the second curve.
3. A small block of mass m slides along a frictionless loop-the-loop track. (a) The block is released from rest at point P.
Calculate the net force acting on it at point Q. (b) Calculate the height above the bottom of the loop from which the
block should be released so that it is on the verge of losing contact with the track at the top of the loop.
4. A 3.0 kg object is moving along the x-axis in a region where its potential energy as a function of x is given as U(x) =
4.0x2, where U is in joules and x is in meters. When the object passes the point x = -0.50 m, its velocity is +2.0 m/s. all
forces acting on the object are conservative.
(a) Calculate the total mechanical energy of the object.
(b) Calculate the x-coordinate of any points at which the object has zero kinetic energy
(c) Calculate the velocity of the object at x = 0.60 m
5. A force acts on a 3.0 kg particle in such a way that the position of the particle as a function of time is given by
X = 3.0t – 4.0t2 + t3, where x is in meters and t is in seconds. Calculate the work done by the force during the first 4.0 s.
FRQ Practice
6. A 0.20 kg object moves along a straight line. The net force acting on the
object varies with the object’s displacement as shown in the graph above.
The object starts from rest at displacement x = 0 and time t = 0 and is
displaced a distance of 20 m. Determine each of the following.
(a) The acceleration of the particle when its displacement x is 6 m. (Ans: 20
m/s2)
(b) The time taken for the object to be displaced the first 12 m (Ans: 1.1 s)
(c) The amount of work done by the net force in displacing the object the
first 12 m. (Ans: 48 J)
(d) The speed of the object at displacement x = 12 m. (Ans: 22 m/s)
(e) The final speed of the object at displacement x = 20 m (Ans: 25.3 m/s)
7. A 0.40 kg object moves in a straight line under the action of a net force. The
graph shows the velocity as a function of time for the object during a 25 s
interval. At time t=0, the object is at the position x=0.
(a) sketch a graph of the acceleration as a function of time for the object.
(b) Calculate the position of the object at t=5.0 s (Ans: 25 m )
(c) On which segment (A,B,C)of the graph is the net force on the object zero?
Justify your answer. (Ans: B be sure you know why)
(d) Calculate the net force on the object during the first 3.0 s of the motion. (Ans:
0.80 N)
(e) Calculate the amount of work done on the object by the net force during the first 15.0 s of the motion. (Ans: 20 J)
(f) For the interval t=15s to t = 25s, is the work done on the object by the net force positive, negative, or zero? Justify
your answer (Ans: negative – be sure you know why and can justify)
8.
A 10 kg block is pushed along a rough horizontal surface by a constant horizontal force F as shown above. At time t = 0,
the velocity v of the block is 6.0 m/s in the same direction as the force. The coefficient of sliding friction is 0.2.
a. Calculate the force F necessary to keep the velocity constant Ans: 19.6 N
The force is now changed to a larger constant value F’. The block accelerates so that its kinetic energy increases by 60 J
while it slides a distance of 4.0 m.
b. Calculate the force F’. Ans: 34.6 N
c. Calculate the acceleration of the block Ans: 3.46 m/s2
9.
A block of mass m slides up the incline shown above with an initial speed vo in the position shown.
a. If the incline is frictionless, determine the maximum height H to which the block will rise, in terms of the given
quantities and appropriate constants.
b. If the incline is rough with the coefficient of sliding friction μ, determine the maximum height to which the block will
rise in terms of H and the given quantities