If the kinetic energy of a 0.62kg stone is 2.3J at its highest point and 9.4J at its lowest point how do I calculate the height at the highest point.
Thanks
The difference in KEnergy has to be equal to the change in gravitational PE.
mgh = 9.4-2.3
0.62*9.8*h= 7.1
solve for h in meters.
To calculate the height at the highest point, you need to understand the relationship between kinetic energy (KE), potential energy (PE), and gravitational potential energy (GPE).
At its highest point, the stone has its maximum gravitational potential energy and zero kinetic energy. The kinetic energy at the highest point is 2.3 J, and at the lowest point, it is 9.4 J.
The change in kinetic energy from the lowest point to the highest point is given by:
ΔKE = KE_lowest - KE_highest
Substituting the given values, we have:
ΔKE = 9.4 J - 2.3 J
ΔKE = 7.1 J
Now, we know that the change in kinetic energy is equal to the change in gravitational potential energy:
ΔPE = ΔKE
Gravitational potential energy is given by the equation:
PE = mgh
where m is the mass of the stone, g is the acceleration due to gravity (approximately 9.8 m/s² on Earth), and h is the height.
Substituting the given values and rearranging the equation, we have:
0.62 kg * 9.8 m/s² * h = 7.1 J
Simplifying the equation further:
6.076 kg·m/s² * h = 7.1 J
Dividing both sides of the equation by 6.076 kg·m/s², we can solve for h:
h = 7.1 J / 6.076 kg·m/s²
h ≈ 1.17 meters
Therefore, the height at the highest point is approximately 1.17 meters.