Question

consider the diagram. the kinetic energy and the potential energy of a roller coaster car at various locations are shown. the total mechanical energy of the car at position d is ______ joules.
a. 0
b. 50000
c. 100000
d. 150000
e. 250000
f. 400000
g. 2000000
h. 2400000
i. none of these.
a ke = 100000 j pe = 300000 j
b ke = 200000 j pe = 200000 j
c ke = 400000 j pe = 0 j
d ke = 250000 j pe = 150000 j
e ke = 320000 j pe = 80000 j
f ke = 400000 j pe = 0 j

Explanation:

Step1: Calculate total mechanical energy at position A

Total mechanical energy \(E = KE + PE\). At position A, \(KE = 100000\space J\) and \(PE=300000\space J\). So \(E = 100000 + 300000=400000\space J\).

Step2: Check conservation of mechanical energy

Assuming no non - conservative forces (like friction, air resistance) act on the roller - coaster car (implied by the problem structure of showing \(KE\) and \(PE\) values at different positions), the total mechanical energy \(E = KE+PE\) is conserved.

Step3: Calculate total mechanical energy at position D

At position D, \(KE = 250000\space J\) and \(PE = 150000\space J\). Using \(E=KE + PE\), we get \(E=250000+150000 = 400000\space J\).

Answer:

f. 400000