Dynamics - Work and Energy
Problem Description
Problem 1:
The crate has a mass of 111 kg and is at rest when it is subjected to the action of the two forces; FA= 200N directed down at qA = 37deg and FB = 1028 N directed upwards at qB = 22deg as shown.
Determine (a) the distance it slides in order to reach a speed of 5 m/s and (b) the time it takes to reach this speed. The coefficient of friction between the crate and the surface is mu = 0.21.
Problem 2:
The force F = 52s2 is applied to the 31 kg block, directed as shown, theta = 38deg. At s=0, the block is moving to the right at 2 m/s. Determine (a) the velocity of the block when s = 4 m and (b) the acceleration at this instant. The coefficient of kinetic friction between the block and the surface is muk = 0.12.
Problem 3:
The two blocks A and B have weights WA = 294 lbs and WB = 33 lbs. Starting from rest, the block A attains a speed of 5 ft/s after traveling 8 ft down the incline having an angle theta = 45 deg. Determine the (a) the time to reach this speed and (b) the kinetic coefficient of friction between the incline and block A, muk.
Problem 4:
A vehicle has a weight of 28800 lbs and an engine which transmits a constant power of 330 bhp to all four wheels. Determine (a) the vehicle's maximum constant speed while climbing a 7 percent incline and (b) the maximum incline while traveling at a constant 72 mph.
Problem 5:
The elevator E and its freight have a total mass of 1210 kg. Hoisting is provided by a motor with a 70 kW nameplate rating and the 322 kg counter-poise C. If the motor is drawing electric power equal to its nameplate rating while hoisting the elevator at a constant 4.4 mps speed, (a) determine the overall motor efficiency.
Also (b) determine the maximum speed if the efficiency were 100%.
Problem 6:
The 3 lb collar is released from rest at A and travels along the smooth guide. Determine the speed of the collar just before it strikes the stop at B. The spring constant is 3 lb/in and has an unstretched length of 10 inches. R = 14 inches and ht = 16 inches.
Problem 7:
Two uncompressed springs of equal length having stiffness kA = 270 N/m and kB= 710 N/m are 'nested' together to form a shock absorber. A 7 kg block dropped from an at rest position above the top of the springs causes the springs to compress 630 mm at the instant the block momentarily stops. (a) Determine the height of the block above the springs. (b) Now repeat this problem and determine the height of the block, but assume the two springs are pre-compressed 315 mm just before the block is dropped.
Problem 8:
A tank car coasting freely and horizontally at 4 ft/s is stopped by two spring bumpers A and B having constants kA = 24400 lbs/ft and kB = 44400 lb/ft. If the two springs are initially uncompressed and the change in 'the length of the spring assembly at the instant the car stops is 33.23 inches, determine (a) the weight of the tank car. Now (b) assume each spring is preloaded to F1 = 9500 lbs and determine the Weight of the tank car.
