Answer:
At point A;
GPE = 58800 J
KE = 0 J
At point B;
GPE = 44100 J
KE = 14700 J
At point C;
GPE = 0 J
KE = 58800 J
At point D;
GPE = 29400 J
KE = 29400 J
EPE = 29400 J.
Step-by-step explanation:
The Gravitational Potential Energy, GPE, is given as follows;
GPE = The mass. m × The acceleration due to gravity, g × The elevation or height, h
∴ GPE = m × g × h
The Kinetic Energy, KE = 1/2 × The mass × The square of the velocity, v²
KE = 1/2 × m × v²
At point A;
The parameters are;
h = 100m, v = 0 (Starting point), Cart mass, m = 60 kg, we have;
GPE = m × g × h = 60 × 9.8 × 100 = 58800
GPE = 58800 J
KE = 1/2 × m × v² = 1/2 × 60 × 0² = 0
KE = 0 J
Mechanical Energy, ME = GPE + KE = 58800 + 0 = 58800 = Constant
ME = 58800 J
At point B;
GPE = 60 × 9.8 × 75 = 44100
GPE = 44100 J
KE = ME - GPE = 58800 - 44100 = 14700
KE = 14700 J
At point C;
GPE = 60 × 9.8 × 0 = 0 J
KE = ME - GPE = 58800 - 0 = 58800
KE = 58800 J
At point D;
v = 0, the Cart is brought to rest by the spring
GPE = 60 × 9.8 × 50 = 29400
GPE = 29400 J
KE = ME - GPE = 58800 - 29400 = 29400
KE = 29400 J
The Elastic Potential Energy EPE gained by the spring = KE = 29400
EPE = 29400 J.