PHY 113, Summer 2007
Langenbrunner
HW 8 – due Tuesday, June 19
1. A 2140 kg railroad flatcar, which can move with negligible friction, is motionless next to a platform. A 242 kg sumo wrestler runs at 5.3 m/s along the platform (parallel to the track) and then jumps onto the flatcar. What is the speed of the flatcar if he then
a) stands on it,
b) runs at 5.3 m/s relative to it in his original direction,
c) turns and runs at 5.3 m/s relative to the flatcar opposite his original direction?
2. At the instant a 3.0 kg particle has a velocity of 6.0 m/s in the negative y direction, a 4.0 kg particle has a velocity of 7.0 m/s in the positive y direction. What is the speed of the center of mass of the two-particle system?
3. In the overhead view below, five forces of the same magnitude act on a merry-go-round for the strange; it is a square that can rotate about point P at midlength along one of the edges. Rank the forces acting on it according to the magnitude of the torque they create about point P, greatest first. (Sorry about the bad photocopying.)
4. In the figure below, two blocks, of mass m1 = 400 g and m2 = 600 g, are connected by a massless cord that is wrapped around a uniform disk of mass M = 500 g and radius R = 12.0 cm. The disk can rotate without friction about a fixed horizontal axis through its center; the cord cannot slip on the disk. The system is released from rest. Find
a) the magnitude of the acceleration of the system of the blocks,
b) the tension T1 in the cord at the left,
c) the tension T2 in the cord at the right.
5. Starting from rest at t=0, a wheel undergoes a constant angular acceleration. When t = 2.0 s, the angular velocity of the wheel is 5.0 rad/s. The acceleration continues until t = 20 s, when it abruptly ceases. Through what angle does the wheel rotate in the interval t=0 to t = 40 s?
6. The rigid body shown below consists of three particles connected by massless rods. It is to be rotated about an axis perpendicular to its plane through point P. If M = 0.40 kg, a = 30 cm, and b = 50 cm, what is the moment of inertia of this rigid body?
7. A wheel turns at constant angular acceleration through 90 rev in 15 s, reaching an angular speed of 10 rev/s.
a) What is its angular speed at the beginning of the 15 s interval?
b) How much time elapses between the time the wheel is at rest and the beginning of the 15 s interval?
8. The picture below shows the massive shield door at a neutron test facility at Lawrence Livermore Laboratory; this is the world’s heaviest hinged door. The door has a mass of 44,000 kg, a rotational inertia about a vertical axis through its huge hinges of 8.7x104 kg*m2, and a (front) face width of 2.4 m. Neglecting friction, what steady force, applied at its outer edge and perpendicular to the plane of the door, can move it from rest through an angle of 90 degrees in 30 s?
9. I own a very strange meter stick. It IS one meter long, but it has a (nonconstant) linear density of λ(x) = x (kg/m2), where x is the distance measured from the end.
a) At what millimeter marker is the center of mass located?
b) If I were to rotate this meter stick about an axis through the end (corresponding to x=0), what would the moment of inertia be?