36. A bead of mass m � 5.00 kg is released from point Aand slides on the frictionless track shown in
Figure P5.36. Determine (a) the bead’s speed at points B and C and (b) the net work done by the force of
gravity in moving the bead from A to C.
39. The launching mechanism of a toy gun consists of a spring of unknown spring constant, as shown in
Figure P5.39a. If the spring is compressed a distance of 0.120 m and the gun fired vertically as shown, the
gun can launch a 20.0-g projectile from rest to a maximum height of 20.0 m above the starting point of the
projectile. Neglecting all resistive forces, (a) describe the mechanical energy transformations that occur
from the time the gun is fired until the projectile reaches its maxi- mum height, (b) determine the spring
constant, and (c) find the speed of the projectile as it moves through the equilibrium position of the spring
(where x � 0), as shown in Figure P5.39b
46. A child of mass m starts from rest and slides without friction from a height h along a curved waterslide (Fig.
P5.46). She is launched from a height h/5 into the pool. (a) Is mechanical energy conserved? Why? (b) Give the
gravitational potential energy associated with the child and her kinetic energy in terms of mgh at the following
positions: the top of the waterslide, the launching point, and the point where she lands in the pool. (c) Determine
her initial speed v0 at the launch point in terms of g and h. (d) Determine her maximum airborne height ymax in
terms of h, g, and the horizontal speed at that height, v0x. (e) Use the x-component of the answer to part (c) to eliminate v0 from the answer to part (d), giving the height ymax in terms of g, h, and the launch angle u. (f) Would your
answers be the same if the waterslide were not frictionless? Explain.
52.
While running, a person dissipates about 0.60 J of mechanical energy per step per kilogram of body mass. If a
60-kg person develops a power of 70 W during a race, how fast is the person running? (Assume a running step is 1.5 m
long.)
53. The electric motor of a model train accelerates the train from rest to 0.620 m/s in 21.0 ms. The total mass of the
train is 875 g. Find the average power delivered to the train during its acceleration.
58. A 650-kg elevator starts from rest and moves upward for 3.00 s with constant acceleration until it reaches its
cruising speed, 1.75 m/s. (a) What is the average power of the elevator motor during this period? (b) How does this
amount of power compare with its power during an upward trip with constant speed?
59.
The force acting on a particle varies as in Figure P5.59. Find the work done by the force as the particle moves (a) from
x = 0 to x = 8.00 m, (b) from x = 8.00 m to x = 10.0 m, and (c) from x = 0 to x= 10.0 m.
81. A child’s pogo stick (Fig. P5.81) stores energy in a spring (k = 2.50 x104 N/m). At position A(x1 = -0.100 m), the
spring compression is a maximum and the child is momentarily at rest. At position AB (x =0), the spring is relaxed and
the child is moving upward. At position C, the child is again momentarily at rest at the top of the jump. Assuming that
the combined mass of child and pogo stick is 25.0 kg, (a) calculate the total energy of the system if both potential
energies are zero at x =0, (b) determine x2, (c) calculate the speed of the child at x = 0, (d) determine the value of x for
which the kinetic energy of the system is a maximum, and (e) obtain the child’s maximum upward speed.
89. Three objects with masses m1 � 5.0 kg, m2 � 10 kg, and m3 � 15 kg, respectively, are attached by strings over frictionless pulleys as indicated in Figure P5.89. The horizon- tal surface exerts a force of friction of 30 N on m2. If the
system is released from rest, use energy concepts to find the speed of m3 after it moves down 4.0 m.
m2