Answer the following Potential Energy and Energy Conservation problems: a. Two b
ID: 1624637 • Letter: A
Question
Answer the following Potential Energy and Energy Conservation problems: a. Two blocks with different masses are attached to either end of a light rope that passes over a light, frictionless pulley suspended from the ceiling. The masses are released from rest, and the more massive one starts to descend. After this block has descended 1.20 m, its speed is 3.00 m/s. If the total mass of the two blocks is 15.0 kg, what is the mass of each block? b. On a horizontal surface, a crate with mass 50.0 kg is placed against a spring that stores 360 J of energy. The spring is released, and the crate slides 5.60 m before coming to rest. What is the speed of the crate when it is 2.00 m from its initial position? Answer the following Work and Kinetic Energy problems: a. You are asked to design spring bumpers for the walls of a parking garage. A freely rolling 1200-kg car moving at 0.65 m/s is to compress the spring no more than 0.090 m before stopping. What should be the force constant of the spring? Assume that the spring has negligible mass. b. On an essentially frictionless, horizontal ice rink, a skater moving at 3.0 m/s encounters a rough patch that reduces her speed to 1.65 m s due to a friction force that is 25% of her weight. Use the work-energy theorem to find the length of this rough patch.Explanation / Answer
The negative work done by the spring equals the change in kinetic energy of the car
The work done by a spring when it is compressed a distancex
from equilibrium is
1/2 k x^2 = K2 - K1
k = m v1^2/x1^2
= 1200 ( 0.65)^2/0.090^2
=62592.59 N/m