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You are riding on a roller coaster at your favorite amusement park. Now you are riding down the hill, enjoying the speed at which you are moving and you are at the point where in the next second, you will be going back up hill. Determine the energy type that exists at that moment, is it potential or kinetic energy? The mass of the cart with everyone in it is 12.5 kg, at its maximum speed it travels 16.3 m/s and the height of the hill is 13.5 m. Calculate the energy the cart has at that moment.
To determine the energy type that exists at the moment when the cart is about to go back uphill, we need to consider the height and speed of the cart.
Step 1: Calculate the potential energy (PE) of the cart using the formula:
PE = m * g * h
where m is the mass of the cart, g is the acceleration due to gravity (9.8 m/s^2), and h is the height of the hill.
PE = 12.5 kg * 9.8 m/s^2 * 13.5 m
PE = 1661.25 Joules
Step 2: Calculate the kinetic energy (KE) of the cart using the formula:
KE = (1/2) * m * v^2
where m is the mass of the cart and v is the speed of the cart.
KE = (1/2) * 12.5 kg * (16.3 m/s)^2
KE = 3374.625 Joules
Step 3: Determine the energy type at that moment.
Comparing the potential energy and kinetic energy, we see that the cart has a greater amount of kinetic energy (3374.625 Joules) compared to potential energy (1661.25 Joules). Therefore, at that moment, the energy type that exists is kinetic energy.
Answer: The energy at that moment is kinetic energy with a value of 3374.6 Joules.