A 6kg cat is running across a table which is 1.2 m tall. The kinetic energy of the cat is 48 j.
A) how fast is the cat running?
B) what is the potential energy of the cat?
C) what is the total mechanical energy of the cat?
I will be happy to critique your thinking on this.
To find the answers to these questions, we can use the formulas for kinetic energy, potential energy, and total energy.
A) To find the speed at which the cat is running, we can use the formula for kinetic energy:
Kinetic Energy (KE) = (1/2) * mass * velocity^2
Given that the mass of the cat is 6 kg and the kinetic energy is 48 J, we can rearrange the formula to solve for velocity:
48 J = (1/2) * 6 kg * velocity^2
Simplifying the equation, we have:
48 J = 3 kg * velocity^2
Dividing both sides of the equation by 3 kg, we get:
velocity^2 = 16 J/kg
Taking the square root of both sides, we find:
velocity ≈ 4 m/s
So, the cat is running at approximately 4 m/s.
B) To find the potential energy of the cat, we use the formula:
Potential Energy (PE) = mass * gravity * height
Given that the mass of the cat is 6 kg, the height of the table is 1.2 m, and the acceleration due to gravity is approximately 9.8 m/s^2, we can calculate the potential energy:
PE = 6 kg * 9.8 m/s^2 * 1.2 m
PE ≈ 70.56 J
Therefore, the potential energy of the cat is approximately 70.56 J.
C) The total mechanical energy of the cat is the sum of its kinetic energy and potential energy:
Total Energy = Kinetic Energy + Potential Energy
Total Energy = 48 J + 70.56 J
Total Energy ≈ 118.56 J
Hence, the total mechanical energy of the cat is approximately 118.56 J.