Change of gravitational potential energy

[jcamaross]

Homework Statement

An ATV(all terrain Vehicle) of 2000kg mass moves up a 15 degree slope at constant speed os 6m/s. What is the rate of change of gravitational potential energy with time. note power= change of U/change t

a 5.25 kw
b 24.8 kw
c 30.4kw
d 118 kw

Homework Equations

The Attempt at a Solution

no idea

 

[Liquidxlax]

well you know your potential energy equation i'd hope

just in case

U=mgh where m is the mass g is gravity h is height and U is potential

the change in potential is one potential minus another.

what height do you start at, what is your potential at a new height and how long did it take to get there.oh yeah and kinetic energy is k=.5mv^2

use K=.5mv^2 and U=mgh with a little trig and you golden

 

[jcamaross]

thanks a lot

 

[jcamaross]

i still have no idea!

 

[rwisz]

I would approach this problem by first defining the relevant equations and concepts. The change in gravitational potential energy (U) is equal to the product of the mass (m), acceleration due to gravity (g), and change in height (h): U = mgh. In this case, the ATV is moving at a constant speed, so there is no change in kinetic energy and the only energy being considered is gravitational potential energy. Therefore, the rate of change of gravitational potential energy with time can be calculated using the formula for power: P = ΔU/Δt. Plugging in the given values, we get P = (2000 kg)(9.8 m/s^2)(sin 15°)(6 m/s) = 58800 W = 58.8 kW.

Out of the given options, the closest answer is option b (24.8 kW). However, this does not take into account the mass of the ATV and the angle of the slope, so it is not the correct answer. Therefore, the correct answer would be none of the given options, as it is approximately 58.8 kW.