How Do You Calculate Gravitational Potential Energy on an Inclined Plane?

[dance_sg]

Homework Statement

A 50.0 kg carton is dragged up a low-friction plank onto the back of the truck. The length of the plank is 3.00 m and it makes an angle of 15.0º with the ground. With respect to the bottom of the plank, the gravitational potential energy of the carton on the truck is

Homework Equations

ep=mgh

The Attempt at a Solution

im not sure what i have to do with the 15 degrees in order for me to solve the equation.

 

[kuruman]

Use the angle to find the change in height of the block. A block moving up a 30^o ramp of fixed length (3.0 m) rises higher vertically than if the angle is 15^o.

 

[tomcue]

Gravitational potential energy is the energy an object possesses due to its position in a gravitational field. In this case, the carton is being lifted to a higher position on the truck, so its gravitational potential energy is increasing.

To solve for the gravitational potential energy, we can use the equation ep=mgh, where m is the mass of the carton, g is the acceleration due to gravity (9.8 m/s^2), and h is the height the carton is lifted.

In this scenario, the height h is equal to the vertical distance the carton is lifted, which is given by the length of the plank (3.00 m) multiplied by the sine of the angle it makes with the ground (15.0º). This can be written as h = 3.00 m * sin(15.0º).

Substituting the values into the equation, we get:

ep = (50.0 kg) * (9.8 m/s^2) * (3.00 m * sin(15.0º)) = 72.1 J

Therefore, the gravitational potential energy of the carton on the truck, with respect to the bottom of the plank, is 72.1 J. This means that if the carton were to be released from this position, it would have 72.1 J of energy as it falls back to the ground.