4. An 800.0 kg roller coaster car is at rest at the top of a 95 m hill. It rolls down the first drop to a height of 31 m. When it travels to the top of the second hill, it is moving at 28 m/s. It then rolls down the second hill until it is at ground level.Calculate the kinetic and potential energy at the top and bottom of each hill
To calculate the kinetic and potential energy at the top and bottom of each hill, we can use the following formulas:
Potential energy (PE) = mass (m) × gravity (g) × height (h)
Kinetic energy (KE) = 0.5 × mass (m) × velocity squared (v^2)
Step 1: Calculate the potential energy at the top of the first hill.
PE1 = m × g × h1
PE1 = 800.0 kg × 9.8 m/s² × 95 m
Step 2: Calculate the kinetic energy at the bottom of the first hill.
KE1 = 0.5 × m × v1²
Since the car starts at rest, v1 = 0
Step 3: Calculate the potential energy at the top of the second hill.
PE2 = m × g × h2
PE2 = 800.0 kg × 9.8 m/s² × 31 m
Step 4: Calculate the kinetic energy at the bottom of the second hill.
KE2 = 0.5 × m × v2²
KE2 = 0.5 × 800.0 kg × (28 m/s)²
Step 5: Calculate the potential energy at the bottom of the second hill.
PE3 = m × g × h3
Since the car is at ground level, h3 = 0
Now, let's plug in the values to calculate the energies:
Step 1: Calculate the potential energy at the top of the first hill.
PE1 = 800.0 kg × 9.8 m/s² × 95 m
Step 2: Calculate the kinetic energy at the bottom of the first hill.
KE1 = 0.5 × 800.0 kg × (0 m/s)²
Step 3: Calculate the potential energy at the top of the second hill.
PE2 = 800.0 kg × 9.8 m/s² × 31 m
Step 4: Calculate the kinetic energy at the bottom of the second hill.
KE2 = 0.5 × 800.0 kg × (28 m/s)²
Step 5: Calculate the potential energy at the bottom of the second hill.
PE3 = 800.0 kg × 9.8 m/s² × 0 m
Simply perform the arithmetic calculations to find the values for each energy.