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# Conservation of Energy

### Conservation of momentum: Example problem

If two objects collide and one is initially at rest, answer the following (ignore any frictional effects): a) Is it possible for both of them to be at rest after the collision? b) Is it possible for one of them to be at rest after the collision? c) Under what condition is their total energy conserved?

### Draw two diagrams for the situation where a moving train collides with a train that is not moving, and the trains use their springy bumpers to bounce off each other without damage. One diagram should show the instant just before the collision and the other the instant just after the collision. Assume the trains do not have the same mass. Make sure you identify your isolated system. Solve for the final velocity of each train in terms of the initial velocity of the initially moving train.

Draw two diagrams for the situation where a moving train collides with a train that is not moving, and the trains use their springy bumpers to bounce off each other without damage. One diagram should show the instant just before the collision and the other the instant just after the collision. Assume the trains do not have the s

### Roller Coaster: Energy Conservation

A roller coaster car starts from rest and rolls down a frictionless track, reaching speed v_f at the bottom. a. If you want the car to go two times as fast at the bottom, by what factor must you increase the height of the track? b. Does the answer to part (a) depend on whether the track is straight or not? Explain.

### Two particles collide. To determine speeds, angles etc after collision.

An atomic nucleus of mass m traveling with speed v collides elastically with a target particle of mass 2m (initially at rest) and is scattered at 90 degree;. a) at what angle does the target particle move after the collision? b) what are the final speeds of the two particles? c) what fraction of the initial kinetic energy is tr

### Potential energy and conservation of energy and linear momentum

1.) The two masses in the Atwood's machine shown in the figure below are initially at rest at the same height. After they are released, the large mass, m2, falls through a height h and hits the floor, and the small mass, m1, rises through a height h. a.) Find the speed of the masses just before m2 lands. Assume the ropes and

### 2D motion of a projectile

A block of mass m slides down a frictionless incline. The block is released at height h above the bottom of the loop (see file for drawing of path). a. What is the force on the inclined track on the block at point A b. What is the force on the inclined track at point B c. At what speed does the block leave the track at poin

### Fresnel's equations to calculate the ratio

A linearly polarized electromagnetic wave is incident on the plane interface between air and an isotropic medium of relative permittivity &#949; = 3 and relative permeability &#956; = 1. The incident propagation vector makes an angle of 60o with the normal to the interface and the direction of polarization of the incident wave i

### Calculations for Work, Potential Energy, and Power

An iron ball having a mass of 5 kg is lifted from the floor to a height of 2.5 meters above the floor. a) How much work was done to lift the ball? b) How much potential energy did the ball gain? c) If the motor lifting the ball raises it 2.5 meters in ten seconds, what is its power? If a 600 kg car is moving with a s

### Skate Boarder's Projectile Motion

The drawing shows a skateboarder moving at 5.4 m/s along a horizontal section of a track that is slanted upward by 48 degrees above the horizontal at its end, which is 0.40 m above the ground. When she leaves the track, she follows the characteristic path of projectile motion. Ignoring friction and air resistance, find the maxim

### Rotational kinetic energy and spring

Please see attachment. Thank You your help is greatly needed! 24. A 2.5-kg ball and a 5.0-kg ball have an elastic collision. Before the collision, the 2.5-kg ball was at rest and the other ball had a speed of 3.5 m/s. What is the kinetic energy of the 2.5-kg ball after the collision? 25. A 50-kg rider on a moped of mass 75

### An electron moving to the left at 0.8c collides with an incoming photon moving to the right. After the collision, the electron is moving to the right at 0.6c and an outgoing photon moves to the left. What was the wavelength of the incoming photon?

An electron moving to the left at 0.8c collides with an incoming photon moving to the right. After the collision, the electron is moving to the right at 0.6c and an outgoing photon moves to the left. What was the wavelength of the incoming photon?

### Calculations with a Ballistic Pendulum

In a ballistic pendulum an object of mass m is fired with an initial speed v_0 at a pendulum bob. The bob has a mass M, which is suspended by a rod of length L and negligible mass. After the collision, the pendulum and object stick together and swing to a maximum angular displacement theta as shown a). Find an expression for

### Energy Conservation

Nonliving and living factors that contribute to or are affected by the energy conservation problem.

### Electric Potential Difference Created by Point Charges

I have a test coming up and I can't seem to grasp the concept of this particular part of the chapter. Here are two sample problems that I am having the most difficulty with. 1.) One particle has a mass of 3.00 10-3 kg and a charge of +7.60 µC. A second particle has a mass of 6.00 10-3 kg and the same charge. The two parti

### Rotational mechanics: Find the translational speed at the top

A bowling ball encounters a 0.760 m verticle rise on the way back to ball rack. Ignore frictional losses and assume that the speed of the ball is 3.50 m/s at the bottom of the rise. .

### Simple harmonic motion

Please see attached file for detailed description. 34. Block rests on a frictionless horizontal surface and is attached to a spring. When set into simple harmonic motion, the block oscillates back and forth with an angular frequency of 7.0 rad/s. The drawing indicates the position of the block when the spring is unstrained. T

### Momentum and Angular Momentum

Consider a small frictionless puck perched at the top of a fixed sphere of radius R. If the puck is given a tiny nudge so that is begins to slide down, through what vertical hight will it descend before it leaves the surface of the sphere?[Hint: Use conservation of energy to find the puck's speed as a function of its height, the

### Work, Energy, and Momentum

1. An iron ball having a mass of 5 kg is lifted from the floor to a height of 2.5 meters above the floor. a) How much work was done to lift the ball? b) How much potential energy did the ball gain? 2. If a 600 kg car is moving with a speed of 25 m/s, that what is its kinetic energy? Put your answer in Joules.

### The Lagrangian Formulation of Mechanics

A ring of mass m slides on a smooth vertical rod. Attached to the ring is a light, inextensible string passing over a smooth peg located distance a from the rod. At the other end of the string is a mass M (M > m). The ring is released from rest at the same level as the peg. Determine, in terms of M,a, and m, the maximum distance

### ball and ring roll down a ramp

A ball and a ring, both of the same mass are released from rest, at the same time, and allowed to roll down a ramp. The top of the ramp is at height (h). There is no mention of any friction. Which object will reach the bottom of the ramp first?

### work done

An 80 kg jogger starts from rest and runs up the hill into a stiff breeze. At the top of the hill the joggers body has done a work of 1.8 X 10^4 J, air resistance has done work of 4420J, and the joggers speed is 3.5 m/s. (1) Is the work done by the joggers body positive or negative? I this work done by a conservative or non-c

### Inelastic collision and ballistic pendulum

- A 38g bullet is fired at a stationary bag which is hanging vertically from the ceiling. The speed of the bullet is 180m/s. If the mass of the bag is 5.0kg, what is the maximum height it will reach? - A spring is compress 8.7cm between two carts of 1.0kg and 1.5kg respectively. If the spring constant is 89N/m what is the vel

### Potential Energy & Energy Conservation - Springs

An 80kg man jumps from a height of 2.5m onto a platform mounted on springs. The spring compress 0.240 below its initial position and then it rebounds. Platform & spring have negligible mass. a) What is the spring's force constant? b) What is his speed when the spring is compressed 0.120m? c) If he gently steps on the plat

### Collision of particles with symmetry due to interaction.

This question concerns a collision of two identical particles, A and B, each of mass m, which constitute an isolated system that is observed from an inertial frame. Assume that the particles, when sufficiently close, interact only through a potential energy function. At an instant long before the collision (when the distance bet

### Physics Home Experiment: Conservation of energy and momentum

Home Experiment 1 PURPOSE This experiment was designed to understand and confirm the conservation of energy and the conservation of momentum. Part I - Conservation of Energy Equipment Setup Slotted plastic ruler Steel ball bearing Put the ruler at a shallow incline on a table or a chair. Your setup should look somethi

### The Speed of the Bullet Before It Hit the Block

A 2.00-g bullet hits and becomes embedded in a 5.00-kg wood block which is hanging from a 1.20-m long string. This causes the block to swing to a height of 2.24mm. What was the speed of the bullet before it hit the block?

### Speed of Solid Disk Rolling Down an Incline

A solid disk is released from rest and rolls without slipping down an inclined plane that makes an angle of 25.0 with the horizontal. What is the speed of the disk after it has rolled 3.00 m, measured along the plane? 3.53 m/s 4.07 m/s 5.71 m/s 6.29 m/s.

### Conservation of momentum and energy, rotation.

1. The 20-lb cart B is supported on rollers of negligible size. If a 10-lb suitcase A is thrown horizontally on it at 10 ft/s, determine the time t and the distance B moves before A stops relative to B. The coefficient of kinetic friction between A and B is &#956;k =0.4. 2. Determine the magnitude of the angular momentum of

### Objectives of a Marketing Campaign

Based on the information given in the following scenario, I need help answering the three questions at the end of the scenario: Clif Bar and Co., which makes Energy-bar, is taking its concern about global warming to the ski slopes in a Save Our Snow Winter Roadtrip. The van, powered by vegetable oil, will visit ski areas and