A pole-vaulter has 3500J of energy when he crosses a bar 7 meters high. How much kinetic energy will he have just before he reaches the ground ( assuming no friction) ?
To find the kinetic energy (KE) of the pole-vaulter just before he reaches the ground, we can use the principle of conservation of energy. The total mechanical energy at any point during the motion is constant, which means the sum of potential energy (PE) and kinetic energy (KE) remains the same.
So, at the highest point (crossing the bar 7 meters high), all the energy is in the form of potential energy. Therefore, we can equate the initial potential energy (PE) to the final kinetic energy (KE) to find the answer.
Initial potential energy (PE) = Final kinetic energy (KE)
We can calculate the initial potential energy using the formula:
PE = mgh
Where:
m = mass of the pole-vaulter
g = acceleration due to gravity (approximately 9.8 m/s²)
h = height (7 meters)
Since we don't have information about the mass of the pole-vaulter, we cannot determine the exact value of kinetic energy. However, we can still calculate the potential energy at the top and know that it will be equal to the kinetic energy at the bottom of the jump.
Assuming the mass of the pole-vaulter is 70 kg, we can calculate the potential energy at the top:
PE = mgh
PE = 70 kg * 9.8 m/s² * 7 m
PE = 4,893 J
So, the kinetic energy just before the pole-vaulter reaches the ground will also be approximately 4,893 J.
To determine the kinetic energy of the pole-vaulter just before reaching the ground, we need to understand the concept of mechanical energy conservation. Mechanical energy is the sum of potential energy and kinetic energy.
1. Start by calculating the potential energy at the peak of the jump. The formula for potential energy is given by:
Potential Energy (PE) = mass * gravity * height
Given that the pole-vaulter has crossed a 7-meter high bar, we can assume that the potential energy at the peak is:
PE = m * g * h
= m * 9.8 * 7
= 68.6 * m (where m is the mass; we can ignore the units for now)
2. Apply the law of conservation of mechanical energy, which states that mechanical energy is conserved in a system where there is no external work or friction. Therefore, the initial total mechanical energy (potential energy + kinetic energy) is equal to the final total mechanical energy.
Initial total mechanical energy = Final total mechanical energy
Initially, when the pole-vaulter crosses the bar, all the energy is potential energy:
Initial total mechanical energy = Potential Energy
= 3500J
At the final moment just before reaching the ground, all the initial potential energy would have transformed into kinetic energy.
Final total mechanical energy = Kinetic Energy
3. Therefore, the kinetic energy just before the pole-vaulter reaches the ground is equal to the initial potential energy:
Kinetic Energy = Final total mechanical energy
= Initial total mechanical energy
= 3500J
So, the pole-vaulter will have 3500J of kinetic energy just before reaching the ground, assuming there is no friction or external work.
Why would the total energy change if there is no friction?
At the top he has potential energy due to height but not much kinetic, only that due to his horizontal velocity which is low.
When he comes down he gains kinetic but loses the same amount of potential.