Question

A 2100 kg vehicle is traveling at 80 m/s at a decline of 1700 meters. Calculate the mechanical energy, the potential energy, and the kinetic energy of the vehicle.

Answer 1

the mechanical energy : 40,623,900 J

the potential energy : 33,903,900 J

the kinetic energy : 6,720,000 J

Step-by-step explanation:

To calculate the mechanical energy, potential energy, and kinetic energy of the vehicle, we can use the following formulas:

Mechanical Energy (ME) = Potential Energy (PE) + Kinetic Energy (KE)

Potential Energy (PE) = mgh

Kinetic Energy (KE) = 1/2mv^2

where m is the mass of the vehicle, g is the acceleration due to gravity (9.81 m/s^2), h is the height of the decline, and v is the velocity of the vehicle.

Given:

m = 2100 kg

v = 80 m/s

h = 1700 m

g = 9.81 m/s^2

Potential Energy (PE) = mgh = 2100 kg x 9.81 m/s^2 x 1700 m = 33,903,900 J

Kinetic Energy (KE) = 1/2mv^2 = 1/2 x 2100 kg x (80 m/s)^2 = 6,720,000 J

Mechanical Energy (ME) = Potential Energy (PE) + Kinetic Energy (KE) = 33,903,900 J + 6,720,000 J = 40,623,900 J