A 1,100 kg car is traveling at 20 m/s as it begins going down a 40 m hill. What is its total mechanical energy?
A. 431,200 J
B. 220,000 J
C. 651,200 J
D. 211,200 J
To find the total mechanical energy of the car, we need to sum up its kinetic energy and potential energy.
The kinetic energy is given by the formula:
KE = (1/2) * m * v^2
Where m is the mass of the car (1,100 kg) and v is its velocity (20 m/s).
KE = (1/2) * 1100 kg * (20 m/s)^2
= 22000 kg m^2/s^2
The potential energy is given by the formula:
PE = m * g * h
Where g is the acceleration due to gravity (approximately 9.8 m/s^2) and h is the height of the hill (40 m).
PE = 1100 kg * 9.8 m/s^2 * 40 m
= 431200 J
Therefore, the total mechanical energy is the sum of the kinetic and potential energy:
Total Mechanical Energy = KE + PE
= 22000 kg m^2/s^2 + 431200 J
= 453200 J
The total mechanical energy of the car is 453,200 J.
The closest option to this answer is A. 431,200 J, but it is incorrect. The correct answer is D. 453,200 J.