Okay. How do I go about answering this question? And what is it really asking?
A watermelon has a mass of 118 kg. It is on a platform 5 m above the ground. When taken off the platform, it is allowed to slide down a ramp. How high above the ground is the watermelon at the moment its kinetic energy 4.61 kJ?
The initial potential energy of the watermelon is mass*acceleration*height or mgh for Earth. For practical purposes assume that total energy of the watermelon is constant. So the potential energy + the kinetic energy is constant. The kinetic energy is given at the point of interest. So the remaining potential energy is:
(118kg * g * 5m) - 4.61kj = ?
After you solve for the remaining potential energy, just use mgh again:
mgh = remaining potential energy
solve for h
Also, it is assumed there is no friction with the ramp.
To answer the question, we need to determine the height above the ground at which the watermelon is located when its kinetic energy is 4.61 kJ.
To do this, we can make use of the principle of conservation of energy. In this case, the total mechanical energy of the watermelon is conserved as it slides down the ramp. Initially, the watermelon is at a certain height on the platform, and when it reaches the ground, its kinetic energy is a given value of 4.61 kJ.
To solve for the height, we need to consider two types of energy: gravitational potential energy and kinetic energy.
Gravitational potential energy (PE) can be calculated using the formula:
PE = m * g * h
where m is the mass of the watermelon, g is the acceleration due to gravity, and h is the height above the ground.
Kinetic energy (KE) can be calculated using the formula:
KE = (1/2) * m * v^2
where m is the mass of the watermelon and v is its velocity.
In this question, we are given the mass of the watermelon (118 kg) and the kinetic energy when it reaches the ground (4.61 kJ). We also know that the watermelon fell from a height of 5 m.
To find the velocity of the watermelon when it reaches the ground, we can rearrange the formula for KE:
v = √(2 * KE / m)
Now, let's substitute the given values into the equations and calculate the height above the ground at the moment when the kinetic energy is 4.61 kJ.
PE = m * g * h
PE = 118 kg * 9.8 m/s^2 * 5 m
PE = 5790 J
Next, we calculate the velocity using the given kinetic energy:
v = √(2 * KE / m)
v = √(2 * 4.61 kJ / 118 kg)
v ≈ √39.0684 m^2/s^2
v ≈ 6.25 m/s (rounded to two decimal places)
Finally, we can calculate the height above the ground (h) using the formulas for kinetic and potential energy:
KE = (1/2) * m * v^2
4.61 kJ = (1/2) * 118 kg * (6.25 m/s)^2
4.61 kJ = 0.5 * 118 kg * 39.0625 m^2/s^2
4.61 kJ = 2309.84375 J
Now, we can rearrange the formula for potential energy and solve for h:
h = PE / (m * g)
h = 2309.84375 J / (118 kg * 9.8 m/s^2)
h ≈ 2.01 m (rounded to two decimal places)
Therefore, at the moment the watermelon's kinetic energy is 4.61 kJ, it is approximately 2.01 meters above the ground.