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Students are asked to design a bumper to attach to a cart in a collision so that the force between the carts is decreased by a factor of 5 when a collision is staged as shown below. Note that ${ M }_{ 2 }$ is held in position by the wall and the bumper is attached to the front of that cart.

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In order to do this, which of the following procedures should they utilize?


Measure how far the moving cart on the left moves after the impact and use that to determine the acceleration and net force on the cart. Graph the change in velocity vs. distance moved. Repeat the trial with the bumper and start from the same position on the ramp.


Measure the angle of the ramp and the mass of the cart that is rolling down the ramp. Calculate the component of the force of gravity moving the cart down the ramp. Graph gravity vs. angle. Repeat with the moving cart on the ramp with a different angle when using the bumper and compare until the component of gravity is one-fifth​.


Use a force sensor on the moving cart to graph the force of impact versus time without a bumper and then repeat the trial with the bumper. The area of the force vs. time graph is the change in momentum. Be sure to start the cart on the ramp at the same position each time. Extending the time by a factor of five will reduce the force by a factor of five.


Roll the cart down the ramp and measure how far the cart on the right moves toward the wall. Start the moving cart further up the ramp when using the bumper until the stationary cart moves five times the distance. The change in energy is the force times distance so that five times the distance is one-fifth​ the force.

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