ME 577 – Human Motion Kinetics Homework #2 Solutions Posted 1/26/2018

1. In the re-worked Star Trek that came out in 2009, there is a scene where Mr. Kirk (played by Chris Pine) and Mr. Sulu (played by John Cho) fight Romulans on the surface of some kind of laser drill. The physics of the laser drill are beyond the scope of this particular course, but you may wish to bring it up with someone in the Physics department. At one point Mr. Sulu falls off the drill. He does the smart thing and spreads his arms and legs to create drag and, hopefully, control his descent. Kirk then tries to save him by literally diving off the laser drill, streamlining his flight, and catching up to Mr. Sulu.

Here we are going to start with a simple problem. Namely, we will determine the terminal velocity of each character. If we assume that both heroes have masses around 80kg, then the only real difference between Mr. Sulu's fall and Mr. Kirk's fall is the cross sectional area they present to the wind. For Mr. Sulu, this is approximately 0.6m2 while for Kirk, it is a much smaller 0.058m2. Compute their relative velocities at impact (assuming they reach terminal velocity before impact).

2. In the first Iron Man movie, Tony Stark wearing his boot jets (not the full suit) can hover in the air using only 1% of Tmax (the maximum thrust in each boot jet) in each boot. In this instance he weighs approximately 200 lbs.

Determine the value of Tmax.

If Iron Man (person + armor) has a weight of 425 lbs. and he applies the maximum boot thrust so that he travels straight up, determine his initial acceleration.

1 3. Given that the kinetic energy of a particle, T, is mv• v, show that the time derivative of T is 2 ∑F • v (4 points).

nd 4. Beginning with Newton’s 2 Law, derive the work-energy theorem. 5. Assume that a fastball is thrown, the batter misses, and the catcher stops the ball. We want to estimate the force the ball exerts on the catcher’s glove. Let’s assume that the ball is thrown at 90 mph and has a mass of approximately 145 grams. Calculate its kinetic energy. If the catcher stops the ball over a distance of 12 cm, what is the average force required to stop the ball? Please include a free body diagram in your solution.

Twins catcher, Joe Mauer

Plot the average force against the stopping distance (between 2 and 12 cm).

What if the velocity of the baseball is increased to 99 mph. and everything else stays the same? What is the average force required to stop the ball?

6. Two ice skaters start out motionless in the center of an ice rink. They then push each other apart. The male partner has a mass of 80 kg and moves to the left at a speed of 1.5 m/s. If the female partner has a mass of 58 kg, how fast does she move? Which direction does she move? What is the change in momentum of the two skaters? What is the change in energy of the two skaters?

7a. If a baseball is thrown at a batter’s head and hits him in the helmet, the helmet can compress a maximum distance of 0.5 inches. What average force would be required to stop the baseball? Say it travels at 90 mph.

7b. What if it is a softball thrown at 75 mph?