2008
to P1112
Fall stretch, and comes to rest just as he reaches the water surface. If Freddie's mass is m, and the bungee cord is massless, which of the following expressions is/are true? (Neglect effects due to the air.) (A) mg = kL (B) mg = kH (C) mg = k(H - L) (D) mgH = 2 mv1 (E) mgL = 2 mv1 (F)
1 1
2
Homework #9 Reading: 6.5, 7.2-7.5, 8.1-8.3
Not all concepts will be covered in class you are responsible for all material in the reading and in the homework problems.
(G) (H) (I)
mgH = 2 kH
1
1
2 2
Problems: 1. A 2.00-kg package is released on a 53.10 incline, (see Fig.7.43 in the book), 4.00 m from a long spring with force constant 120 N/m that is attached at he bottom of the incline. The coefficient of friction between the package and the incline are s=0.40 and k=0.20. The mass of the spring is negligible. a) what is the speed of the package just before it reaches the spring? b) what is the maximum compression of the spring? c) the package rebounds back up the incline. How close does it get to its initial position? 2. A basketball player, of mass m=70kg, jumps h=1m straight up. Consider only the trajectory until he reaches the top of his jump and neglect friction/drag. (a) How much work is done by the normal force from the floor? (b) How much work is done by gravity? 3. The potential energy of a pair of hydrogen atoms separated by a large distance x is given by U(x) = -C/x6, where C is a positive constant. What is the force that one atom exerts on the other? Is this force attractive or repulsive? 4. Consider the system in shown Fig. 6.37 of your textbook. The rope and the pulley have negligible mass and the pulley is frictionless. The coefficient of kinetic friction between the 8.00-kg block and the tabletop is K=0.250. The blocks are released from rest. Use energy methods to calculate the speed of the 6.00-kg block after it has descended 1.50 m. 5. Freddie Fearless is trying bungee jumping. Starting at the top of a tall tower at height H above a pool of water, Freddie is attached to a bungee cord whose unstretched length is L (< H) and which behaves like an ideal spring of spring constant k when stretched beyond L. Freddie drops from rest from the tower, reaches speed v1 just as the bungee cord begins
mgH = 2 k(H - L) mgL = 2 k(H - L)
1 1
2 2
(J) mg(H - L) = 2 k(H - L) (K) mg(H - L) = 2 kH
2
2
1
2
mg(H - L) = 2 mv1
1
6. The potential energy U(x) of a particle that can move along the x-axis is graphed as a function of the particle's position x. The particle starts at x = - 0.4 m moving in the +x direction () with kinetic energy 4.0 J, and it makes it all the way to x = + 0.4 m. U(x) (J)
3 2 1 0 -1 -2 -3 -0.4 -0.3 -0.2 -0.1 +x (m)
0
0.1
0.2
0.3
0.4
For each question below, please give the entire range of answers that apply: (a) Where does the particle experience zero force? (b) Where does the particle experience a force acting in the +x direction ()? (c) Where is the particle moving fastest? (d) When the particle reaches x = + 0.1 m, how much energy must be taken away from it so that it will be confined to x + 0.2 m?