Which of the following has the greatest gravitational potential energy?
a 20-Metric Ton Container lifted at 5 meters
a 25-kg projectile at 5,200 meter altitude
a 300-kg helicopter at 1.5-km altitude moving at 60km per hour
an 35-Metric Ton train cruising on a 4.73-meter overpass moving at 40km per hour
None enough data to create a conclusion
The gravitational potential energy of an object depends on its mass, height, and the acceleration due to gravity.
To determine which of the given options has the greatest gravitational potential energy, we need to calculate the potential energy for each option using the formula:
GPE = mass * height * gravity
1. 20-Metric Ton Container lifted at 5 meters:
Mass = 20,000 kg
Height = 5 meters
2. 25-kg projectile at 5,200 meter altitude:
Mass = 25 kg
Height = 5,200 meters
3. 300-kg helicopter at 1.5-km altitude moving at 60km per hour:
Mass = 300 kg
Height = 1,500 meters
4. 35-Metric Ton train cruising on a 4.73-meter overpass moving at 40km per hour:
Mass = 35,000 kg
Height = 4.73 meters
Since we have all the necessary data, we can now calculate the gravitational potential energies for each option and compare them.
1. GPE (Container) = 20,000 kg * 5 m * 9.8 m/s^2 = 980,000 J
2. GPE (Projectile) = 25 kg * 5,200 m * 9.8 m/s^2 = 1,274,000 J
3. GPE (Helicopter) = 300 kg * 1,500 m * 9.8 m/s^2 = 4,410,000 J
4. GPE (Train) = 35,000 kg * 4.73 m * 9.8 m/s^2 = 1,656,710 J
Comparing the values obtained, we can see that option 3, the 300-kg helicopter at 1.5-km altitude moving at 60km per hour, has the greatest gravitational potential energy with a value of 4,410,000 J.
To determine which object has the greatest gravitational potential energy, we need to calculate the potential energy for each object using the formula:
Potential Energy = mass x g x height
where:
mass is the mass of the object (in kilograms),
g is the acceleration due to gravity (approximately 9.8 m/s^2 on Earth),
and height is the altitude or height at which the object is located (in meters).
Let's calculate the potential energy for each object:
1. 20-Metric Ton Container lifted at 5 meters:
mass = 20,000 kg (1 metric ton = 1,000 kg)
g = 9.8 m/s^2
height = 5 m
Potential Energy = 20,000 kg x 9.8 m/s^2 x 5 m
= 980,000 J (Joules)
2. 25-kg projectile at 5,200 meter altitude:
mass = 25 kg
g = 9.8 m/s^2
height = 5,200 m
Potential Energy = 25 kg x 9.8 m/s^2 x 5,200 m
= 1,274,000 J
3. 300-kg helicopter at 1.5-km altitude moving at 60 km/h:
mass = 300 kg
g = 9.8 m/s^2
height = 1.5 km (1 kilometer = 1,000 meters)
Potential Energy = 300 kg x 9.8 m/s^2 x 1,500 m
= 4,410,000 J
4. 35-Metric Ton train cruising on a 4.73-meter overpass moving at 40 km/h:
mass = 35,000 kg (1 metric ton = 1,000 kg)
g = 9.8 m/s^2
height = 4.73 m
Potential Energy = 35,000 kg x 9.8 m/s^2 x 4.73 m
= 1,725,170 J
Comparing the potential energy values calculated for each object, we see that the 300-kg helicopter at 1.5-km altitude moving at 60 km/h has the greatest gravitational potential energy of 4,410,000 J. Therefore, the helicopter has the greatest gravitational potential energy out of the options given.