You have been chosen as the test subject for the newest attraction at Canada’s Wonderland. This attraction is a single-person roller coaster ride that has a 25.0 m drop followed by a plunger/piston device that brings the ride to rest. The plunger/piston is connected to a cylinder that contains 250 kg of water. The cart has a mass of 75.0 kg and starts at rest from the top of the track. To determine the total mass of the cart during the ride you must add your mass. As the cart moves down the track it has been determined that friction in the wheels and axles results in the production of 2750 J of thermal and sound energy combined. The plunger/piston at the bottom of the device has been designed to stop the cart with a maximum
You have been chosen as the test subject for the newest attraction at Canada’s Wonderland. This attraction is a single-person roller coaster ride that has a 25.0 m drop followed by a plunger/piston device that brings the ride to rest. The plunger/piston is connected to a cylinder that contains 250 kg of water. The cart has a mass of 75.0 kg and starts at rest from the top of the track. To determine the total mass of the cart during the ride you must add your mass. As the cart moves down the track it has been determined that friction in the wheels and axles results in the production of 2750 J of thermal and sound energy combined. The plunger/piston at the bottom of the device has been designed to stop the cart with a maximum acceleration of 5.00 g’s (i.e. 49.0 m/s2).
MY MASS: 66.2kg
Problem 1:
The cart with you inside of it starts from rest at the top of the ride.
Determine the gravitational potential energy of the cart with you as the single passenger at the top of the ride.
Problem 2:
As the cart moves down the track, gravitational potential energy is converted into kinetic energy, thermal energy and sound energy.
Determine the kinetic energy of the cart at the bottom of the cart.
Problem 3:
In order to stop the ride, the cart collides with the plunger/piston system applying a force to it. According to Newton’s 3rd law the piston will apply the same force back on the cart. This force cannot exceed 5.00 g’s (or 49.0 m/s2) without the passenger losing consciousness. Use Newton’s 2nd law to determine the magnitude of this force.
Determine the maximum force exerted on the cart by the plunger/piston system.
Problem 4:
The remaining kinetic energy of the cart is removed as work is done pushing in the plunger/piston and compressing the water inside the cylinder. Use the work equation to determine the displacement of the plunger/piston.
Determine the displacement of the plunger/piston as it compresses the water inside the cylinder.
Problem 5:
The work done by the plunger/piston in compressing the water inside the cylinder is converted into thermal energy within the water. If the specific heat capacity of water is 4184 J/kg°C, then determine the temperature change of the water in the cylinder as it brings the cart to rest (assuming 100% energy transfer efficiency).
Determine temperature change of the water inside the cylinder.
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