A 1.47-newton baseball is dropped from a height of 10.0 meters and falls through the air to the ground. The kinetic energy of the ball is 12.0 joules the instant before the ball strikes the ground. The maximum amount of mechanical energy converted to internal energy during the fall is_________.
I need help to solve this and I can’t get the answer when I tried:(
To solve this problem, we can use the principle of conservation of mechanical energy, which states that the total mechanical energy of a system remains constant if no external forces are acting on it.
The mechanical energy of a falling object is given by the sum of its potential energy and kinetic energy. The potential energy at a given height (h) is given by the equation:
PE = mgh
Where:
- PE is the potential energy
- m is the mass of the object
- g is the acceleration due to gravity
- h is the height of the object
Given that the baseball has a mass of 1.47 newtons and is dropped from a height of 10.0 meters, we can calculate its potential energy as follows:
PE = (1.47 N) * (10.0 m) * (9.8 m/s^2)
= 144.06 joules
Since the kinetic energy of the ball is given as 12.0 joules right before it hits the ground, the difference between the initial potential energy and the final kinetic energy represents the amount of energy converted to internal energy during the fall:
Energy Converted = Initial Potential Energy - Final Kinetic Energy
= 144.06 joules - 12.0 joules
= 132.06 joules
Therefore, the maximum amount of mechanical energy converted to internal energy during the fall is 132.06 joules.
To solve this problem, we need to use the principle of conservation of mechanical energy. According to this principle, the total mechanical energy of an object remains constant as long as only conservative forces (such as gravity) are at work.
Let's break down the problem step by step:
1. Determine the initial mechanical energy of the baseball when it is dropped.
The initial mechanical energy can be calculated using the formula:
Ei = PEi + Ki
where Ei is the initial mechanical energy, PEi is the initial potential energy, and Ki is the initial kinetic energy.
Since the ball is dropped, potential energy is converted entirely to kinetic energy, so PEi = 0. Thus, Ei = Ki.
2. Calculate the final mechanical energy of the baseball just before it hits the ground.
The final mechanical energy, Ef, can be calculated as the sum of the gravitational potential energy and the kinetic energy just before hitting the ground.
Ef = PEf + Kf
Since the ball is at a height of 10.0 meters, PEf = m * g * h, where m is the mass of the baseball, g is the acceleration due to gravity (9.8 m/s²), and h is the height (10.0 meters).
Given the mass of the baseball is not provided, we can't determine PEf directly. However, we know that Ef = 12.0 J (kinetic energy just before striking the ground).
3. Find the maximum amount of mechanical energy converted to internal energy during the fall.
The maximum amount of mechanical energy converted to internal energy is given by ΔE = Ei - Ef
ΔE = Ei - Ef
But since Ei = Ef, the mechanical energy converted to internal energy is zero.
Therefore, the maximum amount of mechanical energy converted to internal energy during the fall is zero.
Ok so like people view this yet can’t help me I don’t understand
the potential energy before the drop is ... m g h ... 1.47 N * 10.0 m ... 14.7 J
it appears that 2.7 J is converted to internal energy ... 14.7 - 12.0