Homework Ch. 8 Conservation of Energy - Due M 4/2 in class.
PHY 161 General Physics I: Mechanics and Thermodynamics
Physics Department --- Mercer University --- Spring 2007
PLEASE NOTE: The instructor’s preference is that your homework solutions be handwritten on printed
copies of these pages and/or blank standard printer paper sheets (8 ½” x 11”), front and back... But if
absolutely necessary, you may use notebook pages; in that case, please remove the paper fringes.
FOR THIS ENTIRE PROBLEM SET, use energy methods whenever possible, rather than using
kinematics and/or Newton’s Laws.
1. An ideal Atwood’s machine (massless and frictionless pulley) has unknown masses m1 and
m2. The masses are released from rest, and reach a speed of 2 m/s after moving through 1.5
m, at which time the kinetic energy of the system is 30 J. Find the masses m1 and m2.
2. A ball with mass m = 4 kg is attached to two identical springs on a frictionless floor. Each
has spring constant k = 200 N/m; each has equilibrium length λ = 0.6 m. The springs are
attached to two walls separated by a distance L = 1 m. Define x to be the ball’s distance from
the left wall.
a) Find an expression for the total potential energy of the ball as a function of x. I.e. find the
constants U0, K and x0 such that U(x) = U0 + ½ K(x-x0)2.
b) If we hold the ball at x = 0.2 m and release it, what will be its maximum speed v?
3. On a level tabletop are placed two springs oriented horizontally a distance D = 1.5 m apart.
They have spring constants k1 = 300 N/m and unknown k2. The coefficient of kinetic friction
μκ between a block and the tabletop is also unknown. The block has mass m = 4 kg and its
size is negligible. It is placed on the table, compressing spring #1 by x1 = 60 cm. The block is
released and it slides across the table; it compresses spring #2 by a maximum amount x2 =
33.3 cm. The block then slides back across the table, but only travels away from spring #2 by
a distance d = 0.295 m before it stops. It never reaches spring #1 again…
a) What is the unknown spring constant k2?
b) What is the unknown coefficient of kinetic friction μκ?
c) If the mass of the block were instead m’ = 0.5 kg, what would be the maximum
compression x2’ of spring #2?
4. A ball with mass m = 3 kg is dropped vertically through the air from its initial height H0 =
2.5 m onto a platform which is attached to a spring with spring constant k = 200 N/m. While
it is falling through the air it experiences a resistive force fA. While it is on the spring
platform (and moving up or down) it experiences a different resistive force fP. The maximum
compression of the spring is d = 0.95 m. The ball then moves upward again, leaving the
platform to reach a maximum height H = 1.8 m.
a) Using the variables defined above, write down the conservation of energy equation for the
ball’s motion from the initial height H0 to the maximum compression d. Do the same for the
motion from maximum compression d to final height H. Do the same for the motion from
initial height H0 to final height H.
b) Find the values of fA and fP.
c) How much energy was “lost” to the resistive forces during the ball’s entire motion?
d) If the ball is then allowed to continue moving, it will again fall onto the spring platform
and will again rise through the air. What will be the new maximum compression dnew? What
will be the new maximum height Hnew?