2011

Honors Take Home Assignment #2

Name______

Hour______

Score____/107 pts

1.  A person who weighs 670 N steps onto a spring scale in the bathroom, and the spring compresses by 0.79 cm.

  1. What is the spring constant? ( 5pts)
  1. What is the weight of another person who compresses the spring by 0.34cm? ( 5pts)

2.  A block of mass m=0.95 kg is fastened to an unstrained horizontal spring whose spring constant is k=82 N/m. The block is given a displacement of +0.15 m, where the + sign indicates that the displacement is along the +x axis, and then released from rest.

  1. What is the force (magnitude and direction ) that the spring exerts on the block just before the block is released? ( 5pts)
  1. Find the angular frequency of the resulting oscillation. ( 5pts)
  1. What is the maximum speed of the block? ( 5pts)
  1. Determine the magnitude of the maximum acceleration of the block. ( 5pts)

3.  A person bounces up and down on a trampoline, while always staying in contact with it. The motion is simple harmonic motion, and it takes 1.9s to complete one cycle. The height of each bounce above the equilibrium position is 45 cm.

  1. What is the amplitude? ( 5pts)
  1. What is the angular frequency of the motion? ( 5pts)
  1. What is the maximum speed attained by the person? ( 5pts)

4.  Astronauts on Mars set up a simple pendulum of length 1.2 m. The magnitude of the acceleration due to gravity on Mars is 1/3rd that of Earth. How many seconds does this pendulum take to complete 100 complete cycles? ( 5pts)

5.  The mass of a string is 0.005 kg, and it is stretched so that the tension in it is 180 N. A transverse wave traveling on this string has a frequency of 260 Hz and a wavelength of 0.6 m. What is the length of the string? ( 5pts)

6.  An 0.8 kg object is attached to one end of a spring and the system is set into simple harmonic motion. The displacement x of the object as a function of time is shown.

  1. What is the amplitude of the motion? ( 2pts)
  1. What is the angular frequency? ( 3 pts)
  1. What is the spring constant? ( 5pts)
  1. What is the speed of the object at t=6.0s?( 3pts)
  1. What two times does the object have maximum acceleration ? ( 2pts)

7.  The speed of a transverse wave on a string is 450 m/s, and the wavelength is 0.18 m. The amplitude of the wave is 2 mm.

  1. What is the period for a particle on the string? ( 5pts)
  1. What is the frequency of the wave? ( 5pts)
  1. How much time is required for a particle of the string to move through a total distance of 1.0 km? ( 5pts)

8.  A bock of mass M=5.4 kg, at rest of a horizontal frictionless table, is attached to a rigid support by a spring of constant k=6000 N/m. A bullet of mass m=9.5 g and velocity v of magnitude 630 m/s strikes and is embedded in the block. Assuming the compression of the spring is negligible until the bullet is embedded, determine

(a) the speed of the block immediately after the collision( 5pts)

(b) the amplitude of the resulting simple harmonic motion. ( 5pts)

9.  Calculate the torque for each force acting on the bar shown below. Assume the axis is perpendicular to the page and passes through a point exactly in the middle of the bar, 2 m from either end. In what direction will the object rotate? (7pts)

25.0 N

31o

23o

45o

2.0 m 10.0 N

4.0 m

30.0 N

10.  A pipe contains water at 500000 Pa above atmospheric pressure. If you patch a 4.0 mm diameter hole in the pipe with a piece of bubble gum, how much force must the gum be able to withstand? ( 5pts)

Show Work for Full Credit; Formula, fill in values, answer with correct units