Collected Problems for Test 3

Problem #14(Due 10/16 Wednesday by 8:00 a.m.)
Thor (mass of 62.0 kg) throws a 0.0580 kg snowball with speed of 33.0 m/s at Loki. Loki (mass of 60.0 kg), catches the snowball. Both are on skates. Thor is initially moving forward with a speed of 2.60 m/s, and Loki is initially at rest.
a) Draw a before and after picture of Thor and the snowball.
b) What is the velocity of Thor after he throws the snowball?
c) Draw a before and after picture of Loki and the snowball.
d) What is the velocity of Loki after he catches the snowball?
Disregard any friction.

Problem #15 (Due 10/18 Friday by 8:00 a.m.)
A small raft with a mass of 11.3 kg is coasting from west to east at 73.0 cm/s when it collides with a small 1.25 kg log floating from north to south at 3.60 m/s. If the raft and the log stick together find the magnitude and direction of the velocity of the raft/log combination just after they move off together. Neglect any effects to the drag of the water.
*Make sure you draw your before and after picture for the collision part.

Problem #16 (Due 10/22 Tuesday 8:00 a.m.)
An air-track glider with a mass of 239 g is moving at 0.81 m/s on a 2.4 m long air track. It collides elastically with a 513 g glider at rest in the middle of the track. The end of the track over which the struck glider moves is not level, but slants upward at an angle of 0.70^o with respect to the horizontal. Will the glider reach the end of the track? Neglect the length of the gliders.

Problem #17 (Due 10/29 Tuesday by 8:00 a.m.)
Skee Ball (picture) involves rolling a solid wooden ball 7.6 cm in diameter down an alley 9 ft. long, where the ball is then launched off a short ramp. Highest points are awarded to those who can launch the ball such that is lands in the topmost cylindrical hole (50 points); landing in lower and larger holes is worth fewer points. The launch ramp is 8.5 cm high and the launch ramp slopes at an angle of 40.0^o. From the top of the launch ramp, the location of the 50 point hole is x₅₀ = 42 cm, y₅₀ = 12 cm. An expert makes a 50 point score with one ball. What were the initial linear and angular velocities of the ball at the bottom of the ramp?

Problem #18 (Due 11/1 Friday by 8:00 a.m.)
The large quadriceps muscle in the upper leg terminates at its lower end in a tendon attached to the upper end of the tibia (see figure a). The forces on the lower leg when the leg is extended are modeled as in figure b, where T is the force of tension in the tendon, w is the force of gravity acting on the lower leg, and F is the force of gravity acting on the foot. Find T when the tendon is at an angle of 25.0^o with the tibia, assuming that w = 31.0 N, F = 12.4 N, and the leg is extended at an angle of 40.0^o with the vertical. Assume that the center of gravity of the lower leg is at its center and that the tendon attaches to the lower leg at a point one-fifth of the way down the leg.

Problem #19 (Due 11/5 Tuesday by 8:00 a.m.)
A crane lifts a 180 kg crate upward with an acceleration of 1.1 m/s ² . The cable from the crate passes over a solid cylindrical pulley at the top of the boom. The pulley has a mass of 130 kg. The cable is then wound onto a hollow cylindrical drum that is mounted on the deck of the crane. The mass of the drum is 150 kg, and its radius is 0.76 m. The engine applies a counterclockwise torque to the drum in order to wind up the cable. What is the magnitude of this torque?