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 collision with a plunger attached to a large spring that brings the ride to rest. The plunger/spring mechanism is composed of a large spring with a mass of 62.5 kg made of pure iron..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 to the system. As the cart moves down the track it has been determined that friction in the wheels and axles results in the production of 12750 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). What is your approximate mass in kilograms? MY MASS IS 82 kg 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 (with you as a passenger) 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: When the cart reaches the bottom of the drop it will have kinetic energy (see problem 2). What is the speed of the cart at the instant it reaches the bottom of the track? Determine the instantaneous speed of the cart at the instant it reaches the bottom of the drop. Problem 4: In order to stop the ride, the cart collides with the plunger/spring system, applying a force to it. According to Newton’s 3rd law the piston/spring system 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 maximum force. Determine the maximum force exerted on the cart by the plunger/spring system Problem 5: The remaining kinetic energy of the cart is removed as work is done pushing on the plunger/spring system and compressing the spring. The average force exerted on the spring is exactly half of the maximum force exerted (see problem 4). Use the general work equation to determine the displacement (i.e. compression) of the spring in the plunger/spring system. Determine the amount of displacement of the plunger/spring as it compresses due to the work done on it by the cart and the average force applied. Problem 6: When the spring becomes fully compressed, the kinetic energy of the cart is converted to thermal energy. Ths energy conversion is 95% efficient (i.e. 95% of the kinetic energy is transformed into thermal energy (in the form of sensible heat). Determine the quantity of thermal energy transferred into the spring. Problem 7: When the spring “absorbs” sensible heat from the collision with the cart, this energy will cause the temperature of the spring to change. Use the mass of the pure iron spring and its specific heat capacity to determine the temperature change that results from this energy transfer. Determine the resulting temperature change of the spring due to the sensible heat transfer.
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 collision with a plunger attached to a large spring that brings the ride to rest. The plunger/spring
What is your approximate mass in kilograms?
MY MASS IS 82 kg
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 (with you as a passenger) 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:
When the cart reaches the bottom of the drop it will have kinetic energy (see problem 2). What is the speed of the cart at the instant it reaches the bottom of the track?
Determine the instantaneous speed of the cart at the instant it reaches the bottom of the drop.
Problem 4:
In order to stop the ride, the cart collides with the plunger/spring system, applying a force to it. According to Newton’s 3rd law the piston/spring system 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 maximum force.
Determine the maximum force exerted on the cart by the plunger/spring system
Problem 5:
The remaining kinetic energy of the cart is removed as work is done pushing on the plunger/spring system and compressing the spring. The average force exerted on the spring is exactly half of the maximum force exerted (see problem 4). Use the general work equation to determine the displacement (i.e. compression) of the spring in the plunger/spring system.
Determine the amount of displacement of the plunger/spring as it compresses due to the work done on it by the cart and the average force applied.
Problem 6:
When the spring becomes fully compressed, the kinetic energy of the cart is converted to thermal energy. Ths energy conversion is 95% efficient (i.e. 95% of the kinetic energy is transformed into thermal energy (in the form of sensible heat).
Determine the quantity of thermal energy transferred into the spring.
Problem 7:
When the spring “absorbs” sensible heat from the collision with the cart, this energy will cause the temperature of the spring to change. Use the mass of the pure iron spring and its specific heat capacity to determine the temperature change that results from this energy transfer.
Determine the resulting temperature change of the spring due to the sensible heat transfer.
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