A64kg skateboarder on a 2.0kg skateboard is on top of a ramp with a vertical height of 5.0 m what is the skateboarders maximum kinetic energy at the bottom of the ramp

Ec=3234 J at the bottom of the ramp.

Explanation:

Kinetic energy is a form of energy. It is defined as the energy associated with the bodies that are in motion and this energy depends on the mass and speed of the body.

The kinetic energy is defined as the amount of work necessary to accelerate a body of a certain mass and in rest position, until reaching a certain speed. Once this point has been reached, the amount of accumulated kinetic energy will remain identical unless a change in speed occurs or the body returns to its resting state by applying a force.

Kinetic energy is represented by the following formula:

Ec = ½ mv²

Where Ec is the kinetic energy, which is measured in Joules (J), m is the mass measured in kilograms (kg) and v is the velocity measured in meters over seconds (m/s).

On the other hand, the potential energy is the energy that measures the ability of a system to perform a job based on its position. In other words, this is the energy a body has at a certain height above the ground.

The gravitational potential energy is the energy associated with the gravitational force. This will depend on the relative height of an object at some reference point, the mass, and the force of gravity. So for an object with mass m, at height h, the expression applied to the gravitational energy of the object is:

Ep = m · g · h

Where Ep is the potential energy in joules (J), m is the mass in kilograms (kg) h is the height in meters (m) and g is the acceleration of fall in m / s² (approximately 9.81 m/s²)

Finally, mechanical energy is that which a body or system obtains as a result of the speed of its movement or its specific position, and that is capable of producing mechanical work. So:

Potential energy + kinetic energy = total mechanical energy

The principle of conservation of mechanical energy indicates that the mechanical energy of a body remains constant when all the forces that act on it are conservative (a force is conservative when the work done on a body depends only on the initial and final points and not the path followed to get from one to another.) Therefore, if the potential energy decreases, the kinetic energy will increase. In the same way if the kinetics decrease, the potential energy will increase.

This principle can be applied in this case. By the time it reaches the foot of the ramp, the body has lost all potential energy since it has no height from the ground that is the reference point. But since mechanical energy must remain constant, it follows that all that potential energy must be transformed into kinetic energy.

Therefore the potential energy at the highest point (top of the ramp) is equal to the kinetic energy of the lowest point (bottom of the ramp).

Then, at the top of the ramp, the system lacks movement therefore it only has potential energy due to the height and does not have kinetic energy. You must calculate their potential energy.

Ep=m*h*g

The total mass of a skateboader and a skateboard is 64.0 kg + 2.0 kg = 66.0 kg.

h= 5.0 m

g= 9.81 m/s²

Ep= 66 kg *9.8 m/s²*5.0 m = 3234 J

At the bottom of the ramp, the system reaches its maximum speed and all the potential energy is transformed into kinetic energy. At this time the potential energy is equal to the kinetic, as previously mentioned with the principle of the conservation of mechanical energy.

Finally, Ec=3234 J at the bottom of the ramp.