an automobile to be transported by ship is raised above the dock by a crane. If the gravitational potential energy of the car is 6.6 x 10^4 and the mass is 960 kg how high has the car been lifted?
m times 9.8 times h
960 x 9.8 x h = 6.6 x 10^4
Simplify.
4408 x h = 66000
66000 / 4408 = 14.97
h = 14.97
To determine the height the car has been lifted, we can use the gravitational potential energy formula:
Gravitational Potential Energy (PE) = m * g * h,
where PE is the gravitational potential energy, m is the mass of the car, g is the acceleration due to gravity, and h is the height the car has been lifted.
Given:
PE = 6.6 x 10^4 J
m = 960 kg
g = 9.8 m/s^2
Substituting the given values into the formula, we have:
6.6 x 10^4 J = 960 kg * 9.8 m/s^2 * h
Now we can solve for h:
h = (6.6 x 10^4 J) / (960 kg * 9.8 m/s^2)
h ≈ 6.99 meters
Therefore, the car has been lifted to a height of approximately 6.99 meters.
To determine the height the car has been lifted, we can use the equation for gravitational potential energy:
Gravitational Potential Energy = mass × gravitational acceleration × height
Given:
Gravitational Potential Energy (GPE) = 6.6 × 10^4 J
Mass (m) = 960 kg
Gravitational acceleration (g) = 9.8 m/s^2 (approximately)
Rearranging the equation, we have:
Height (h) = GPE / (mass × gravitational acceleration)
Substituting the given values:
Height (h) = (6.6 × 10^4 J) / (960 kg × 9.8 m/s^2)
Calculating this expression, we find:
Height (h) ≈ 6.78 m
Therefore, the car has been lifted to a height of approximately 6.78 meters.