1. A block of mass m = 0.55 kg is attached to a spring with a force constant 109 N/m is free to move on a frictionless, horizontal surface as in the figure below. The block is released from rest after the spring is stretched at distance A = 0.13 m. (Indicate the direction with the sign of your answer. Assume that the positive direction is to the right).
a) At that instant, find the force on the block.
b) At that instant, find its acceleration
2.The force constant of a spring is 165 N/m.
a) Find the magnitude of the force required to compress the spring by 4.20 cm from its unstretched length.
b) Find the magnitude of the force required to stretch the spring by 7.96 cm from its unstretched length.
3. A slingshot consists of a light leather cup containing a stone. The cup is pulled back against two parallel rubber bands. It takes a force of 15 N to stretch either one of these bands 1.0 cm.
a) What is the potential energy stored in the two bands together when a 44-g stone is placed in the cup and pulled back 0.11-m from the equilibrium position?
b) With what speed does the stone leave the slingshot?
4. A 10.0-g bullet is fired into, and embeds itself in, a 1.95-kg block attached to a spring with a force constant of 16.2 N/m and whose mass is negligible. How far is the spring compressed if the bullet has a speed of 300 m/s just before it strikes the block and the block slides on a frictionless surface? Note: You must use conservation of momentum in this problem because of the inelastic collision between the bullet and block.
5. A man enters a tall tower, needing to know its height. He notes that a long pendulum extends from the ceiling almost to the floor and that its period is 10.5 s.
a) How tall is the tower?
b) If this pendulum is taken to the moon, where the free-fall acceleration is 1.67 m/s2, what is the period there?
6. 10.03 A simple pendulum has a lenght of 52.1 cm and makes 83.8 complete oscillations in 2.00 min.
a) Find the period of the pendulum.
b) Find the value of g at the location of the pendulum.
7. The sunusoidal wave shown in the figure below is traveling in the positive x-direction and has a frequency of 14.5 Hz.
a) Find the amplitude.
b) Find the wavelength.
c) Find the period
d) Find the speed of the wave
8. Light waves are electromagnetic waves that travel at 3.00 x 108 m/s. The eye is most sensitive to light having a wavelength of 5.50 x 107 m.
a) Find the frequency of this light wave.
b) Find its period
9. A circus performer stretches a tightrope between two towers. He strikes one end of the rope and sends a wave along it toward the other tower. He notes that it takes the wave 0.885 s to reach the opposite tower, 20.0 m away. If a 1.00-m length of rope has a mass of 0.360 kg, find the tension in the tightrope.
10. A piano string having a mass per unit length equal to 4.80 x 10-3 kg/m is under a tension of 1,450 N. Find the speed with which a wave travelson this spring.