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?
To find the speed of the cat, we can use the formula for kinetic energy:
Kinetic energy = (1/2) * mass * (velocity)^2
Given that the kinetic energy is 48 J and the mass of the cat is 6 kg, we can rearrange the formula and solve for the velocity:
48 J = (1/2) * 6 kg * velocity^2
96 J = 6 kg * velocity^2
16 J/kg = velocity^2
4 m^2/s^2 = velocity^2
Taking the square root of both sides gives us:
velocity = √(4 m^2/s^2)
velocity = 2 m/s
Therefore, the cat is running at a speed of 2 m/s.
To find the potential energy of the cat, we can use the formula:
Potential energy = mass * gravitational acceleration * height
Given that the mass of the cat is 6 kg, the height of the table is 1.2 m, and the gravitational acceleration is approximately 9.8 m/s^2, we can calculate the potential energy:
Potential energy = 6 kg * 9.8 m/s^2 * 1.2 m
Potential energy = 70.56 J
Therefore, the potential energy of the cat is 70.56 J.
The total mechanical energy of the cat is the sum of its kinetic energy and potential energy. Therefore:
Total mechanical energy = Kinetic energy + Potential energy
Total mechanical energy = 48 J + 70.56 J
Total mechanical energy = 118.56 J
Therefore, the total mechanical energy of the cat is 118.56 J.
To answer these questions, we need to use the formulas for kinetic energy, potential energy, and mechanical energy.
Let's begin with the formula for kinetic energy (KE):
KE = 0.5 * mass * velocity^2
A) To find the speed (velocity) at which the cat is running, we need to rearrange the formula for kinetic energy:
48 J = 0.5 * 6 kg * velocity^2
Divide both sides of the equation by 3:
16 J = 3 kg * velocity^2
Now, isolate velocity^2 by dividing both sides of the equation by 3 kg:
velocity^2 = 16 J / 3 kg
Taking the square root of both sides, we find that the velocity of the cat is approximately 2.54 m/s.
B) To calculate the potential energy (PE) of the cat, we can use the formula:
PE = mass * gravity * height
Given that the cat weighs 6 kg and the table is 1.2 m tall, and assuming the acceleration due to gravity is approximately 9.8 m/s^2, we can substitute these values into the formula:
PE = 6 kg * 9.8 m/s^2 * 1.2 m
PE = 70.56 J
The potential energy of the cat is approximately 70.56 J.
C) The total mechanical energy (ME) of the cat is the sum of its kinetic energy and potential energy:
ME = KE + PE
Using the values we calculated above:
ME = 48 J + 70.56 J
ME = 118.56 J
The total mechanical energy of the cat is approximately 118.56 J.