Gravitational potential energy

In summary, a 50.0 kg carton is lifted onto a truck by being dragged up a 3.00 m plank at an angle of 15.0º with the ground. The gravitational potential energy of the carton on the truck can be found by using the equation ep=mgh, where h is the change in height of the carton. The angle of 15.0º must be taken into consideration when calculating the change in height.
  • #1
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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.
 
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  • #2


Use the angle to find the change in height of the block. A block moving up a 30o ramp of fixed length (3.0 m) rises higher vertically than if the angle is 15o.
 
  • #3


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.
 

1. What is gravitational potential energy?

Gravitational potential energy is the energy an object possesses due to its position in a gravitational field. It is the energy that is required to move an object from its current position to a reference point, usually at infinity, without any acceleration.

2. How is gravitational potential energy calculated?

The gravitational potential energy of an object can be calculated using the formula U = mgh, where U is the potential energy, m is the mass of the object, g is the acceleration due to gravity, and h is the distance from the object to the reference point.

3. What factors affect gravitational potential energy?

The two main factors that affect gravitational potential energy are the mass of the object and its distance from the reference point. The greater the mass and the farther the distance, the higher the potential energy.

4. What is the relationship between gravitational potential energy and kinetic energy?

Gravitational potential energy and kinetic energy are forms of mechanical energy that are interrelated. As an object falls, its potential energy decreases while its kinetic energy increases. At the bottom of its fall, all of its potential energy is converted into kinetic energy.

5. How is gravitational potential energy used in everyday life?

Gravitational potential energy is used in many everyday activities, such as lifting and lowering objects, riding a rollercoaster, or throwing a ball. It is also used in various forms of renewable energy, such as hydroelectric power, where the potential energy of water is converted into kinetic energy to generate electricity.

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