Hi! I have some questions from a study guide in my physics class, and they give me the answer, but I have to show how to get the answer. I did most of them, but need help with this. All I need is a formula, please. :)Thank you! Here it is:
A skier with a mass of 60.0 kg pushes off with a horizontal speed of 3.0 m/s from the top of a snow
covered hill. As he slides down the hill, his height decreases by 42 m over a distance of 100 m of travel.
How much will his kinetic energy increase by the time he reaches the bottom of the hill
The answer is 24696 J.
ΔKE=ΔPE=mgΔh=60•9.8•42 =24696 J
To find out how much the skier's kinetic energy will increase as he slides down the hill, we can use the work-energy principle.
The work-energy principle states that the work done on an object is equal to the change in its kinetic energy. Mathematically, it can be represented as:
Work = Change in Kinetic Energy
The work done on the skier is equal to the force exerted (in the direction of motion) multiplied by the displacement. In this case, since the skier is sliding down the hill, the force exerted is the component of his weight that is parallel to the hill's surface.
As the skier slides down, his height decreases by 42 m over a distance of 100 m. To find the work done on the skier, we need to calculate the force exerted and multiply it by the distance.
1. Calculate the force exerted:
The force exerted on the skier is equal to the component of the skier's weight parallel to the hill's surface. This force can be calculated using the formula:
Force = mass * acceleration
Since the skier is sliding down the hill with a constant speed and in a straight line, there is no acceleration in the horizontal direction, and the force is equal to the weight of the skier:
Force = mass * gravity
Where mass is the skier's mass (60.0 kg) and gravity is the acceleration due to gravity (9.8 m/s^2).
2. Calculate the work done:
The work done on the skier is equal to the force multiplied by the distance:
Work = Force * distance
Where the force is the weight of the skier calculated in step 1, and the distance is the change in height (42 m).
3. Calculate the change in kinetic energy:
The work done on the skier is equal to the change in kinetic energy:
Work = Change in Kinetic Energy
So, rearranging the formula, we can determine the change in kinetic energy:
Change in Kinetic Energy = Work
Plug in the calculated value of work from step 2 to find the change in kinetic energy.
By following these steps, you will be able to find the amount by which the skier's kinetic energy increases as he reaches the bottom of the hill.