A student throws a ball upwards from the ground level where gravitational potential energy is zero. At a height of 15 m, the ball has a potential energy of 60 J, and is moving upwards with a kinetic energy of 40 J. Ignoring air resistance, the maximum height achieved by the ball is most nearly
20
Well, well, well, it seems like we have a ball that is quite the high flyer! Let's see if we can calculate the maximum height it reaches.
We can figure out the maximum height by determining the total mechanical energy of the ball. Mechanical energy consists of both potential energy and kinetic energy.
At the start, the ball has zero potential energy. As it rises to a height of 15 m, it gains 60 J of potential energy. We also know that at this height, the ball has 40 J of kinetic energy.
So, the total mechanical energy at a height of 15 m would be the sum of the potential and kinetic energy:
Total mechanical energy = Potential energy + Kinetic energy
Total mechanical energy = 60 J + 40 J
Total mechanical energy = 100 J
Now, at the maximum height, all the kinetic energy is converted into potential energy, so we can write:
Potential energy at maximum height = Total mechanical energy
So, the potential energy at the maximum height is 100 J.
But wait a minute, we were asked for the maximum height achieved by the ball, not the potential energy. Silly me! I got carried away with the calculations.
So, to answer your question, the maximum height achieved by the ball is 15 meters.
And remember, physics can be a ball, especially when it comes to calculating heights and energies! Keep reaching for the stars!
To find the maximum height achieved by the ball, we need to consider the conservation of mechanical energy.
The total mechanical energy of the ball, ignoring air resistance, is the sum of its kinetic energy and potential energy. Therefore, at any point during its motion, the total mechanical energy remains constant.
Given that the potential energy at a height of 15 m is 60 J and the kinetic energy is 40 J, we can set up the following equation:
Total mechanical energy = Potential energy + Kinetic energy
Total mechanical energy = 60 J + 40 J
Total mechanical energy = 100 J
Since the total mechanical energy remains constant, we can determine the maximum height achieved by finding the point where the potential energy is maximum, i.e., when the kinetic energy is zero.
At the maximum height, the kinetic energy is zero, so the total mechanical energy is equal to the potential energy:
Total mechanical energy = Potential energy
100 J = Potential energy
Therefore, the maximum height achieved by the ball is when the potential energy is equal to 100 J.
To find the maximum height achieved by the ball, we can use the conservation of mechanical energy. The total mechanical energy of the ball remains constant throughout its motion, ignoring any external forces like air resistance.
The mechanical energy of the ball consists of its kinetic energy (KE) and potential energy (PE). At the ground level, the ball has only kinetic energy, so the potential energy is zero. As the ball moves upwards, its potential energy increases while its kinetic energy decreases. At the maximum height, the ball reaches its peak and has no kinetic energy, so all its energy is in the form of potential energy.
Given that the potential energy at a height of 15 m is 60 J, and the kinetic energy at the same height is 40 J, we can set up the equation:
Potential energy (PE) + Kinetic energy (KE) = Total mechanical energy
60 J + 40 J = Total mechanical energy
Total mechanical energy = 100 J
At the maximum height, the ball has no kinetic energy, so all its energy is in the form of potential energy:
Potential energy at the maximum height = Total mechanical energy = 100 J
Therefore, the maximum height achieved by the ball is approximately 100 m.
PE = 60 = m g h = k * 15 ... k = 4
the KE will become PE as the ball rises ... 4 J per meter of height
... the ball will rise another 10 m