3. Two masses of 1 kg and 0.5 kg are connected as in figure. The mass on the table is connected to a spring withspring constant k-80. The pulley is frictionless. The 0.5 kg mass is drop from rest at a height of 1 m from the floor.At this position the spring is in equilibrium A) Find the velocity as a function of height for the system. B) Find theacceleration.

Answered: 3. Two masses of I kg and 0.5 kg are…

College Physics

1st Edition

ISBN:9781938168000

Author:Paul Peter Urone, Roger Hinrichs

Publisher:Paul Peter Urone, Roger Hinrichs

Chapter16: Oscillatory Motion And Waves

Section: Chapter Questions

Problem 4PE: (a) The springs of a pickup truck act like a single spring with a force constant of 1.30105N/m. By...

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A 2.00-kg block hangs without vibrating at the end of a spring (k = 500. N/m) that is attached to the ceiling of an elevator car. The car is rising with an upward acceleration of g/3 when the acceleration suddenly ceases (at t = 0). (a) What is the angular frequency of oscillation of the block after the acceleration ceases? (b) By what amount is the spring stretched during the time that the elevator car is accelerating?
A 2.00-kg block hangs without vibrating at the end of a spring (k = 500. N/m) that is attached to the ceiling of an elevator car. The car is rising with an upward acceleration of g/3 when the acceleration suddenly ceases (at t = 0). (a) What is the angular frequency of oscillation of the block after the acceleration ceases? (b) By what amount is the spring stretched during the time that the elevator car is accelerating?
A horizontal spring attached to a wall has a force constant of 850 N/m. A block of mass 1.00 kg is attached to the spring and oscillates freely on a horizontal, frictionless surface as in Figure 5.22. The initial goal of this problem is to find the velocity at the equilibrium point after the block is released. (a) What objects constitute the system, and through what forces do they interact? (b) What are the two points of interest? (c) Find the energy stored in the spring when the mass is stretched 6.00 cm from equilibrium and again when the mass passes through equilibrium after being released from rest. (d) Write the conservation of energy equation for this situation and solve it for the speed of the mass as it passes equilibrium. Substitute to obtain a numerical value. (e) What is the speed at the halfway point? Why isnt it half the speed at equilibrium?
In a control system, an accelerometer consists of a 4.70-g object sliding on a calibrated horizontal rail. A low-mass spring attaches the object to a flange at one end of the rail. Grease on the rail makes static friction negligible, but rapidly damps out vibrations of the sliding object. When subject to a steady acceleration of 0.800g, the object should be at a location 0.500 cm away from its equilibrium position. Find the force constant of the spring required for the calibration to be correct.
The length of nylon rope from which a mountain climber is suspended has a force constant of 1.40104N/m. (a) What is the frequency at which he bounces, given his mass plus and me mass of his equipment are 90.0 kg? (b) How much would this rope stretch to break the climber’s fall if he treefalls 2.00 m before the rope runs out of slack? Hint: Use conservation of energy. (c) Repeat both parts of this problem in the situation where twice this length of nylon rope is used.
A particle with a mass of 0.500 kg is attached to a horizontal spring with a force constant of 50.0 N/m. At the moment t = 0, the particle has its maximum speed of 20.0 m/s and is moving to the left. (a) Determine the particles equation of motion, specifying its position as a function of time. (b) Where in the motion is the potential energy three times the kinetic energy? (c) Find the minimum time interval required for the particle to move from x = 0 to x = 1.0 m. (d) Find the length of a simple pendulum with the same period.
In an engine, a piston oscillates with simpler harmonic motion so that its position varies according to the expression x=5.00cos(2t+6) where x is in centimeters and t is in seconds. At t = O. find (a) the position of the particle, (b) its velocity, and (c) its acceleration. Find (d) the period and (e) the amplitude of the motion.
Figure 15.46 This child’s toy relies on springs to keep infants entertained. (credit: By Humboldthead, Flickr) The device pictured in Figure 16.46 entertains infants while keeping them from wandering. The child bounces in a harness suspended from a door frame by a spring constant. (a) If the spring stretches 0.250 m while supporting an 8.0—kg child, what is its spring constant? (b) What is the time for one complete bounce of this child? (c) What is the child's maximum velocity if the amplitude of her bounce is 0.200 m?
Integrated Concepts A toy gun uses a spring with a force constant of 300 N/m to propel a 10.0-g steel ball. If the spring is compressed 7.00 cm and friction is negligible: (a) How much force is needed to compress the spring? (b) To what maximum height can the ball be shot? (c) At what angles above the horizontal may a child aim to hit a target 3.00 m away at the same height as the gun? (d) What is the gun's maximum range on level ground?
(a) The springs of a pickup truck act like a single spring with a force constant of 1.30105N/m. By how much will the truck he depressed by its maximum load of 1000 kg? (b) If the pickup truck has four identical springs, what is the force constant of each?
You attach a block to the bottom end of a spring hanging vertically. You slowly let the block move down and find that it hangs at rest with the spring stretched by 15.0 cm. Next, you lilt the block back up to the initial position and release it from rest with the spring unstretched. What maximum distance does it move dawn? (a) 7.5 cm (b) 15.0 cm (c) 30.0 cm (d) 60.0 cm (e) The distance cannot be determined without knowing the mass and spring constant.
Figure P13.74 shows a crude model of an insect wing. The mass m represents the entire mass of the wing, which pivots about the fulcrum F. The spring represents the surrounding connective tissue. Motion of the wing corresponds to vibration of the spring. Suppose the mass of the wing is 0.30 g and the effective spring constant of the tissue is 4.7 104 N/m. If the mass m moves up and down a distance of 2.0 mm from its position of equilibrium, what is the maximum speed of the outer tip of the wing? Figure P13.74

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