Supposed a skydiver ( mass=75kg ) is falling toward the earth. When the skydiver is 100m above the earth he is moving at 60m/s. At this point calculate the skydiver: Gravitational potential energy
Kinetic energy
Total mechanical energy
To calculate the gravitational potential energy (GPE), kinetic energy (KE), and total mechanical energy of the skydiver at a certain height, we can apply the following formulas:
1. Gravitational Potential Energy (GPE):
GPE = mgh
where:
m = mass of the skydiver
g = acceleration due to gravity (approximately 9.8 m/s²)
h = height above the reference point (in this case, above the earth's surface)
2. Kinetic Energy (KE):
KE = (1/2)mv²
where:
m = mass of the skydiver
v = velocity of the skydiver
3. Total Mechanical Energy (TME):
TME = GPE + KE
Given:
m = 75 kg
h = 100 m
v = 60 m/s
g ≈ 9.8 m/s²
Let's calculate each value step-by-step:
1. Gravitational Potential Energy (GPE):
GPE = mgh
= 75 kg × 9.8 m/s² × 100 m
= 73,500 J (joules)
2. Kinetic Energy (KE):
KE = (1/2)mv²
= (1/2) × 75 kg × (60 m/s)²
= 135,000 J (joules)
3. Total Mechanical Energy (TME):
TME = GPE + KE
= 73,500 J + 135,000 J
= 208,500 J (joules)
Therefore, the calculated values are:
Gravitational potential energy (GPE): 73,500 J
Kinetic energy (KE): 135,000 J
Total mechanical energy (TME): 208,500 J
To calculate the gravitational potential energy, kinetic energy, and total mechanical energy of the skydiver, we need to know the formula for each.
1. Gravitational potential energy (GPE):
The gravitational potential energy of an object near the surface of the Earth is given by the formula:
GPE = m * g * h,
where:
m = mass of the object (in kg)
g = acceleration due to gravity (approximately 9.8 m/s^2 near the surface of the Earth)
h = height above the ground (in meters)
2. Kinetic energy (KE):
The kinetic energy of an object is given by the formula:
KE = (1/2) * m * v^2,
where:
m = mass of the object (in kg)
v = velocity of the object (in m/s)
3. Total mechanical energy:
The total mechanical energy of an object is the sum of its gravitational potential energy and kinetic energy at a particular point. Therefore, we can calculate it by adding the GPE and KE together:
Total mechanical energy = GPE + KE.
In this case, the skydiver's mass (m) is given as 75 kg, and when he is 100m above the Earth, his velocity (v) is given as 60 m/s.
Now let's calculate the values:
1. Gravitational potential energy (GPE):
GPE = m * g * h
GPE = 75 kg * 9.8 m/s^2 * 100 m
GPE = 73,500 Joules
2. Kinetic energy (KE):
KE = (1/2) * m * v^2
KE = (1/2) * 75 kg * (60 m/s)^2
KE = 135,000 Joules
3. Total mechanical energy:
Total mechanical energy = GPE + KE
Total mechanical energy = 73,500 Joules + 135,000 Joules
Total mechanical energy = 208,500 Joules
Therefore, the skydiver's gravitational potential energy is 73,500 Joules, kinetic energy is 135,000 Joules, and total mechanical energy is 208,500 Joules when he is 100 meters above the Earth and moving at 60 m/s.
I’m not understanding your answer
gpe: mass*g*height
KE: 1/2 mass*velocity^2
total ME: add the above