Question

Suppose a car is sitting on a hill 12 meters above the road. The car has a mass of 1,200 kg. The acceleration of the car is 9.8 m/s and the velocity of the car as it begins to roll down the hill is 4.8 m/s. Find the mechanical energy for this scenario.

Answer 1

`154.9KJ`

Step-by-step explanation:

The mechanical Energy associated with a body, is the sum of the potential(Energy due to its position) energy and the kinetic energy(energy due to its motion).Hence ewe can write as

`Mechanical Energy, M.E=Potential Energy(P.E)+Kinetic Energy(K.E)\\`

The expression for the potential Energy is

`P.E=mass*acceleration*height\\P.E=mgh\\`

while the expression for the Kinetic Energy is

`K.E=(1)/(2)*mass*(velocity)^(2)\\K.E=(1/2)mv^(2) \\`

since the Height,h=12m,

mass,m=1200kg,

acceleration,g =9.8

and velocity,v=4.8m/s

we can compute the Mechanical energy in kJ as

`M.E=mgh+(1/2)mv^(2)\\ M.E=(1200*9.8*12) + (1/2)(1200*4.8^(2) )\\M.E=141120 + 13824\\M.E=154944J\\M.E=154.9KJ`