Exam q3
- 1. QUIZ #3: CONSERVATION OF ENERGY ECE A Multiple Choices: 1. How much work is done in raising 1800 lb elevator cab to a height of 90 ft? a. 1.62 x 105 lb-ft b. 2.62 x 105 lb-ft c. 1.60 x 105 lb-ft d. 1.33 x 105 lb-ft 2. In problem #1, how much potential energy does the cab have in its new position? a. Remains the same b. Increased c. Decreased d. Infinite 3. A 180 lb woman runs up a staircase 10 ft high in 6 sec. Find her minimum power output in horsepower. a. 300 hp b. 0.88 hp c. 0.55 hp d. 0.62 hp 4. A motorboat requires 90 hp to move at a constant velocity of 20 mi/hr. How much resistive force does the water exert on the boat at this velocity? a. 1502.3 lbs b. 1702.2 lbs c. 1672.2 lbs d. 1683.7 lbs 5. A man uses horizontal force of 300 N to push a crate up a ramp 8 m long that is 30 deg above the horizontal. How much work does the man perform? a. 2078.5 J b. 2523.1 J c. 2301.2 J d. 2800 J 6. A hoist powered by 35 hp motor is used to raise a 580 kg bucket of concrete to a height of 100 m. If the efficiency is 85%, find the time required. a. 38.3 sec b. 25.64 sec c. 35.2 sec d. 33.8 sec 7. A man skis down a slope of 350 m high. If his velocity is 35 m/s, what percentage of his initial potential energy was lost die to friction and air resistance? a. 17.83% b. 52.8% c. 82.16% d. 74.3% 8. A hammer with a 4-lb head is used to drive a nail into a wooden board. If the hammer is moving at 18 ft/sec when it strikes the nail and the nail moves ¾” into the board, find the average force the hammer exerts on the nail. a. 352.3 lbs b. 420.1 lbs c. 542.1 lbs d. 321.9 lbs 9. A 50 kg crate is pulled up a ramp 20 m long and 5 m high by a constant force 200 N. The crate starts from rest and has a velocity of 3 m/s when it reaches the top of the ramp. What is the frictional force between the crate and the ramp? a. 66.12 N b. 1322.5 N c. 225 N d. 2452.5 N 10. Calculate the work done by the spring when the spring is displaced by 0.05 m. Assuming a spring constant 32 N/m. a. 0.08 J b. 0.04 J c. 0.02 J d. 0.05 J Identification: 1. ____ is the sign convention when the work transferred from the system. 2. ____ is the force law for springs. 3. ____ is the energy associated with the motion of the particle. 4. ____ is the time rate of energy transfer 5. ____ is the metric unit of power 6. ____ is the energy lost because of the friction caused by air. 7. ____ is the energy associated with the arrangement of a system of objects that exerts forces on each other. 8. ____ are forces that cause a change in mechanical energy. 9. ____ states that energy can never be created or destroyed. Energy may be transformed from one form to another, but the total energy of isolated system is always constant. 10. ____ is the energy stored in a spring of force constant k. Problem Solving: 1. Two equal-length springs are “nested” together in order to form a shock absorber. If it is designed to arrest the motion of a 2-kg mass that is dropped s=0.5m above the top of the springs from an at-rest position and the maximum compression of the springs is to be 0.2m, determine the required stiffness of the inner spring, kB, if the outer spring stiffness kA=400 N/m. 2. A roller coaster car is launched at B with a speed sufficient for it to round the top of the loop at C without leaving the track. If the roller coaster car is 200-kg and the velocity at C is 15.66 m/s, determine the velocity at B, assuming that friction and air resistance are negligible. 3. The 0.5-lb ball is shot from the spring device shown. The spring has a stiffness k=10 lb/in and four cords C and plate P keep the spring compressed 2-in when no load is on the plate. The plate is pushed back 3-in from its initial position, so that s=30-in. If it is then released from rest, determine the speed of the ball when it leaves the surface of the smooth inclined plane. BONUS PROBLEM: The 2-kg collar is attached to a spring that has an un-stretched length of 3 m. If the collar is drawn to point B and released from rest, find its speed when it arrives at point A.