Tree Swing An unusual pendulum is made by fixing a string to a horizontal2.cylinder of radius R, wrapping the string several times around the cylinder, and thentying a mass m to the loose end. In equilibrium the mass hangs a distance lo verticallybelow the edge of the cylinder. Find the potential energy if the pendulum has swungangle from the vertical. Show that for small angles, it can be written in theHooke's law form U = k. Comment on the value of k.SSto an

Figure of the unusual pendulum is shown below .

Answered: Tree Swing An unusual pendulum is made…

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter5: Energy

Section: Chapter Questions

Problem 84AP: A cat plays with a toy mouse suspended from a light string of length 1.25 m, rapidly batting the...

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cal energy of the ballEarth sys-tem at the maximum height for each ball. Let y = 0 at the cannon. Review. A bead slides without friction around a loop-the-loop (Fig. P8.5). The bead is released from rest at a height h= 3.50R. (a) What is its speed at point ? (b) How large is the normal force on the bead at point if its mass is 5.00 g?
A child jumps tip and down on a bed, reaching a higher height after each bounce. Explain how the child can increase his maximum gravitational potential energy with each bounce.
A roller-coaster car of mass 1.50 103 kg is initially at the top of a rise at point . It then moves 35.0 m at an angle of 50.0 below the horizontal to a lower point . (a) Find both the potential energy of the system when the car is at points and and the change in potential energy as the car moves from point to point , assuming y = 0 at point . (b) Repeat part (a), this time choosing y = 0 at point , which is another 15.0 m down the same slope from point .
A small block of mass m = 200 g is released from rest at point along the horizontal diameter on the inside of a frictionless, hemispherical bowl of radius R = 30.0 cm (Fig. P8.43). Calculate (a) the gravitational potential energy of the block-Earth system when the block is at point relative to point . (b) the kinetic energy of the block at point . (c) its speed at point B, and (d) its kinetic energy and the potential energy when the block is at point . Figure P8.43 Problems 43 and 44.
A ball is connected to a light spring suspended vertically as shown in Figure 6.17. When pulled downward from its equilibrium position and released, the ball oscillates up and down. (i) In the system of the ball, the spring, and the Earth, what forms of energy are there during the motion? (a) kinetic and elastic potential (b) kinetic and gravitational potential (c) kinetic, elastic potential, and gravitational potential (d) elastic potential and gravitational potential (ii) In the system of the ball and the spring, what forms of energy are there during the motion? Choose from the same possibilities (a) through (d).
A slingshot consists of a light leather cup containing a stone. The cup is pulled back against two parallel rubber bands. It takes a force of 15.0 N to stretch either one of these bands 1.00 cm. (a) What is the potential energy stored in the two bands together when a 50.0-g stone is placed in the cup and pulled back 0.200 m from the equilibrium position? (b) With what speed does the stone leave the slingshot?
A crate on rollers is being pushed without frictional loss of energy across the floor of a freight car (see the following figure). The car is moving to the right with a constant speed v0 . If the crate starts at rest relative to the freight car, then from the work-energy theorem, Fd=mv2/2, where d, the distance the crate moves, and v , the speed of the crate, are both measured relative to the freight car. (a) To an observer at rest beside the tracks, what distance d is the crate pushed when it moves the distance d in the car? (b) What are the crate’s initial and final speeds v0 and v as measured by the observer beside the tracks? (c) Show that Fd=m(v)2/2m(v0)2/2 and, consequently, that work is equal to the change in kinetic energy in both reference systems.
A 2.0-kg block starts with a speed of 10 m/s at the bottom of a plane inclined at 37 to the horizontal. The coefficient of sliding friction between the block and plane is k=0.30 . (a) Use the work-energy principle to determine how far the block slides along the plane before momentarily coming to rest. (b) After stopping, the block slides back down the plane. What is its speed when It reaches the bottom? (Hint: For the round trip, only the force of friction does work on the block.)
A block of mass 500 g is attached to a spring of spring constant 80 N/m (see the following figure). The other end of the spring is attached to a support while the mass rests on a rough surface with a coefficient of friction of 0.20 that is inclined at angle of 300 . The block is pushed along the surface till the spring compresses by 10 cm and is then released from rest. (a) How much potential energy was stored in the block-spring-support system when the block was just released? (b) Determine the speed of the block when it crosses the point when the spring is neither compressed nor stretched. (c) Determine the position of the block where it just comes to rest on its way up the incline.
A slingshot consists of a light leather cup containing a stone. The cup is pulled back against two parallel rubber bands. It takes a force of 15.0 N to stretch either one of these bands 1.00 cm. (a) What is the potential energy stored in the two bands together when a 50.0-g stone is placed in the cup and pulled back 0.200 m from the equilibrium position? (b) With what speed does the stone leave the slingshot?
A child (32 kg) jumps up and down on a trampoline. The trampoline exerts a spring restoring force on the child with a constant of 5000 N/m. At the highest point of the bounce, the child is 1.0 m above the level surface of the trampoline. What is the compression distance of the trampoline? Neglect the bending of the legs or any transfer of energy of the child into the trampoline while jumping.
Review. A 7.80-g bullet moving at 575 m/s strikes the hand of a superhero, causing the hand to move 5.50 cm in the direction of the bullets velocity before stopping. (a) Use work and energy considerations to find the average force that stops the bullet. (b) Assuming the force is constant, determine how much time elapses between the moment the bullet strikes the hand and the moment it stops moving.

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