Download Extra Free Response Questions for Energy (5)

Energy Free Response Test Prep
1. In part of a strongman competition,
the competitors must raise a 50Kg
rock 10meters as quickly as possible,
as shown. The data for the position
of the object as a function of time is
given along with the graph.
a. Manipulate the data to create a
straight line graph. Place this
information in the data table and
graph provided.
b. Determine an equation for the rocks velocity as a function of time
c. Determine the acceleration of the rock
d. Determine the net work done on the rock as it moves from the ground to the 10m mark
e. Determine the energy consumed by the individual to raise the stone (assume 100% efficiency)
f. Determine the power delivered by the person as a function of time
2.
(ENERGY ONLY) A 20Kg block is pulled across a rough floor
as shown. As the block moves, its position in meters can be
tracked as a function of time according to the equation
x=.5t3 + 4t.
a.
b.
c.
d.
What is the starting velocity? (3pts)
Determine each of the following as a function of time.
i. Kinetic energy of box (2pt)
ii. Net force on box (3pts)
iii. Net power provided to box (2pts)
Determine net work done from t=0 to t=2. (4pts)
Circle the correct responses in the following statement.
Friction is performing (positive, zero, or negative) work and the magnitude of work done by friction is
(greater than, equal to, less than) the work done by the pulling force. (3pts)
3. (ENERGY Test Only)An apparatus to determine
coefficients of friction is shown above. The box is slowly
rotated counterclockwise. When the box makes an angle 
with the horizontal, the block of mass m just starts to slide,
and at this instant the box is stopped from rotating. Thus
at angle , the block slides a distance d, hits the spring of
force constant k, and compresses the spring a distance x
before coming to rest. In terms of the given quantities
and fundamental constants, derive an expression for each
of the following.
a. s, the coefficient of static friction
b. E, the loss in total mechanical energy due to friction, of the block-spring system from the start of the
block down the incline to the moment at which it comes to rest on the compressed spring. (not
responsible for this solution when studying for the force quiz)
c. k, the coefficient of kinetic friction.
4. A force sensor (effectively of no mass)
is connected to a pendulum of length L.
The mass of the bob is M. The apparatus
is arranged as shown. The pendulum is
raised to an angle parallel with the ground
(as shown) and released. Solve the
following in terms given variables and
fundamental constants.
a.
Calculate the speed at the bottom
of motion
Calculate the tension at the bottom of motion
Draw the force on the sensor as a function of time for a single oscillation (from release until it arrives back
at the original position). On the graph, the time to return to the original release position is designated
(Tr).
Now imagine we are at angle ѳ at some point while in motion (it has a velocity either up or down
at the moment observed)
d. Draw the direction of the acceleration of the mass M in the position shown on right.
e. Calculate the tension at angle ѳ. ѳ may be a variable in your answer .
b.
c.
5. A spherical, nonrotating planet has a radius R and a uniform density  throughout its volume. Suppose a narrow
tunnel were drilled through the planet along one of its diameters, as shown in the figure above, in which a small ball
of mass m could move freely under the influence of gravity. Let r be the distance of the ball from the center of the
planet.
a. Show that the magnitude of the force on the ball at a distance r < R from the center of the planet is given by
F = -Cr. where C = 4/3(Gm). (3pts)
b.
On the axes below, sketch the force F on the ball as a function of distance r from the center of the planet.
(4pts)
The ball is dropped into the tunnel from rest at point P at the planet's surface.
c. Determine the work done by gravity as the ball moves from the surface to the center of the planet. (3pts)
d.
Determine the speed of the ball when it reaches the center of the planet. (2pts)
e.
Fully describe the subsequent motion of the ball from the time it reaches the center of the planet. (2pts)
f.
Write an equation that could be used to calculate the time it takes the ball to move from point P to the center of
the planet. It is not necessary to solve this equation. (1pt)