Urgent Help Plz ... [Archive]

scjibran

Nov18-07, 01:48 AM

I am stuck on these problems. Just the last 2 ... :mad: :(

any help would be great.

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1. A student stands on a platform that is free to rotate and holds two dumbbells, each at a distance of 65 cm from his central axis. Another student gives him a push and starts the system of student, dumbbells, and platform rotating at 0.80 rev/s. The student on the platform then pulls the dumbbells in close to his chest so that they are each 22 cm from his central axis. Each dumbbell has a mass of 5.00 kg and the rotational inertia of the student, platform, and dumbbells is initially 7.80 kg·m2. Model each arm as a uniform rod of mass 3.00 kg with one end at the central axis; the length of the arm is initially 65 cm and then is reduced to 22 cm. What is his new rate of rotation?

http://i2.photobucket.com/albums/y30/xoxshortie07/fig-085.gif

2. A hydraulic lift is lifting a car that weighs 10 kN. The area of the piston supporting the car is A, the area of the other piston is a, and the ratio A/a is 108.9. How far must the small piston be pushed down to raise the car a distance of 1.6 cm? [Hint: Consider the work to be done.]

dynamicsolo

Nov18-07, 12:12 PM

1. A student stands on a platform that is free to rotate and holds two dumbbells, each at a distance of 65 cm from his central axis. Another student gives him a push and starts the system of student, dumbbells, and platform rotating at 0.80 rev/s. The student on the platform then pulls the dumbbells in close to his chest so that they are each 22 cm from his central axis. Each dumbbell has a mass of 5.00 kg and the rotational inertia of the student, platform, and dumbbells is initially 7.80 kg·m2. Model each arm as a uniform rod of mass 3.00 kg with one end at the central axis; the length of the arm is initially 65 cm and then is reduced to 22 cm. What is his new rate of rotation?

The student with the dumbbells can be considered a "rigid rotator" for the purposes of the problem. Since he's pulling the dumbbells straight toward the rotation axis, no torque is being applied to the system, so angular momentum is conserved. (Alternatively, the torque applied to bring the right-hand dumbbell inward cancels the torque applied to the left-hand one.) What is the angular momentum of a rigidly rotating object?

2. A hydraulic lift is lifting a car that weighs 10 kN. The area of the piston supporting the car is A, the area of the other piston is a, and the ratio A/a is 108.9. How far must the small piston be pushed down to raise the car a distance of 1.6 cm? [Hint: Consider the work to be done.]

What quantity is constant throughout a hydraulic system at a given moment? What will that tell us about the force that must be applied to the car (assume it is raised at constant velocity) and the force that must be applied to the small piston? How much work is done on the car? What does that mean for the distance through which the force on the small piston must be applied?