It shows a ball going along a frictionless track. How do you find the kinetic energy at position B on the track if position B is 15 above the ground and position A is 20 meters above the ground? The weight of the ball is .020 kg
To find the kinetic energy at position B on the track, we can use the principle of conservation of mechanical energy. The mechanical energy of an object is the sum of its potential energy and kinetic energy.
In this case, the potential energy of the ball at position A is due to its height above the ground. The potential energy formula is given by:
Potential energy = mass * gravity * height
Given that the mass of the ball is 0.020 kg, and position A is 20 meters above the ground, we can calculate the potential energy at position A:
Potential energy at A = 0.020 kg * 9.8 m/s^2 * 20 m = 3.92 joules
Since the ball is moving along a frictionless track, there is no loss or gain of mechanical energy. Therefore, the mechanical energy at position A is equal to the mechanical energy at position B.
The mechanical energy at position B is the sum of the potential energy and kinetic energy at that position. Since we are looking for the kinetic energy at position B, we can rearrange the equation:
Kinetic energy at B = Mechanical energy at B - Potential energy at B
Since the mechanical energy is conserved, it remains the same throughout the motion. Therefore, the mechanical energy at B is equal to the initial mechanical energy at A:
Mechanical energy at B = Mechanical energy at A = 3.92 joules
Next, we need to find the potential energy at position B. Given that position B is 15 meters above the ground, the potential energy at B can be calculated using the same formula:
Potential energy at B = 0.020 kg * 9.8 m/s^2 * 15 m = 2.94 joules
Finally, we can substitute the values into the equation to find the kinetic energy at position B:
Kinetic energy at B = Mechanical energy at B - Potential energy at B
Kinetic energy at B = 3.92 joules - 2.94 joules = 0.98 joules
Therefore, the kinetic energy at position B on the track is 0.98 joules.