Unit 7 UT Homework-problems

vijayaraghavan (vv8837) – Unit 7 UT Homework – crane – (23242) 1 This print-out should have 20 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001(part1of2)1.0points A 0 . 48 kg object is attached to a spring with a spring constant 162 N / m so that the object is allowed to move on a horizontal frictionless surface. The object is released from rest when the spring is compressed 0 . 2 m. Find the force on the object when it is released. Answer in units of N. 002(part2of2)1.0points What is the acceleration at this instant? Answer in units of m / s 2 . 003 1.0points A block of mass 3 kg is hung from a spring, causing it to stretch 27 cm at equilibrium, as shown below. The 3 kg block is then replaced by a 4 kg block, and the new block is released from the position shown below, at which point the spring is unstretched. 27 cm y max 3 kg equilbrium 4 kg How far will the 4 kg block fall before its direction is reversed? For the new block case, the total distance of fall is twice the amplitude of the oscillation. The acceleration due to gravity is 9 . 8 m / s 2 . Answer in units of cm. 004 1.0points An automobile having a mass of 430 kg is driven into a brick wall in a safety test. The bumper behaves like a spring of constant 4 . 8 × 10 6 N / m and compresses 3 . 75 cm as the car is brought to rest. What was the speed of the car before im- pact, assuming no energy was lost during im- pact with the wall? Answer in units of m / s. 005(part1of2)1.0points A 0 . 256 kg mass is attached to a spring and executes simple harmonic motion with a pe- riod of 0 . 82 s. The total energy of the system is 4 . 8 J. Find the force constant of the spring. Answer in units of N / m. 006(part2of2)1.0points Find the amplitude of the motion. Answer in units of m. 007 1.0points A 0 . 255 kg mass is attached to a spring and undergoes simple harmonic motion with a pe- riod of 0 . 583 s. The total energy of the system is 3 . 6 J. Find the amplitude of the motion. Answer in units of m. 008(part1of2)1.0points A 1 . 49 kg block at rest on a tabletop is at- tached to a horizontal spring having constant 18 . 9 N / m. The spring is initially unstretched. A constant 23 . 4 N horizontal force is applied to the object causing the spring to stretch. 23 . 4 N 1 . 49 kg 18 . 9 N / m Find the speed of the block after it has moved 0 . 231 m from equilibrium if the sur- face between block and tabletop is frictionless. The acceleration of gravity is 9 . 8 m / s 2 . Answer in units of m / s.

vijayaraghavan (vv8837) – Unit 7 UT Homework – crane – (23242) 2 009(part2of2)1.0points Find the speed of the block after it has moved 0 . 231 m if the coefficient of kinetic friction between block and tabletop is 0 . 113. Answer in units of m / s. 010(part1of2)1.0points A spring with a spring constant of 1 . 9 × 10 2 N/m is attached to a 1.5 kg mass and then set in motion. What is the period of the mass-spring sys- tem? Answer in units of s. 011(part2of2)1.0points What is the frequency of the vibration? Answer in units of Hz. 012(part1of3)1.0points A 622 g mass is connected to a light spring of force constant 5 N / m that is free to oscillate on a horizontal, frictionless track. The mass is displaced 7 cm from the equilibrium point and released from rest. 5 N / m 622 g 7 cm x = 0 x Find the period of the motion. Answer in units of s. 013(part2of3)1.0points What is the maximum speed of the mass? Answer in units of m / s. 014(part3of3)1.0points What is the maximum acceleration of the mass? Answer in units of m / s 2 . 015 1.0points An 86 kg person steps into a car of mass 2630 kg, causing it to sink 7 . 64 cm on its springs. Assuming no damping, with what fre- quency will the car and passenger vibrate on the springs? The acceleration of gravity is 9 . 8 m / s 2 . Answer in units of Hz. 016 1.0points When a mass of 23 g is attached to a certain spring, it makes 25 complete vibrations in 3 . 6 s. What is the spring constant of the spring? Answer in units of N / m. 017 1.0points Consider the simplified single-piston engine in the figure. The piston rod oscillates in simple harmonic motion. The wheel of radius 1 . 83 m rotates at a constant angular speed of 7 . 8 rad / s. a ϖ x = 0 x ( t ) Piston If the piston is fully extended at time t = 0, find the position of the piston at 4 . 28 s. Let the origin ( x = 0) be the center of the wheel. Answer in units of m. 018(part1of2)1.0points A simple pendulum of length of 1 . 58 m and mass of 4 . 8 kg is given an initial speed of 1 . 13 m / s at its equilibrium position. Determine its period (assuming the pendu- lum undergoes simple harmonic motion). The acceleration due to gravity is 9 . 8 m / s 2 . Answer in units of s. 019(part2of2)1.0points Let the zero point of potential energy be where the mass on the pendulum is at its lowest point. Calculate the total energy. Answer in units of J. 020 1.0points Having landed on a newly discovered planet, an astronaut sets up a simple pendulum of