A 1.53-kg ball hangs at the end of a string 1.64 meters in length from the ceiling of a room. The height of the room is 3.77 meters. What is the gravitational potential energy of the ball relative to the floor?
Question
A 1.53-kg ball hangs at the end of a string 1.64 meters in length from the ceiling of a room. The height of the room is 3.77 meters. What is the gravitational potential energy of the ball relative to the floor?
Solution
To calculate the gravitational potential energy of the ball relative to the floor, we need to know the height of the ball above the floor and the mass of the ball. The gravitational potential energy (PE) can be calculated using the formula:
PE = mgh
where: m is the mass of the object (in kg), g is the acceleration due to gravity (approximated as 9.8 m/s² on the surface of the earth), and h is the height of the object above the ground (in m).
First, we need to calculate the height of the ball above the floor. The height of the room is 3.77 meters and the length of the string is 1.64 meters. Therefore, the height of the ball above the floor is:
3.77 m - 1.64 m = 2.13 m
Now we can substitute the values into the formula:
PE = (1.53 kg) * (9.8 m/s²) * (2.13 m) = 31.6 Joules
So, the gravitational potential energy of the ball relative to the floor is approximately 31.6 Joules.
Similar Questions
The diagram at the right shows six positions of a 0.49-kg ball bouncing across a 4.0-meter-high physics room. Information regarding the vertical position is shown. Assume that the floor is the reference level for zero potential energy. Determine the gravitational potential energy of the 0.49-kg ball at position A:
A boy throws a ball up into the air with a speed of 12.3 m/s. The ball has a mass of 0.25 kg. How much gravitational potential energy will the ball have at the top of its flight? (Assume there is no air resistance.)A.12.1 JB.18.9 JC.13.5 JD.20.2 J
A ball of mass 3 kg is kept at a height of 4m above the ground. Find the potential energy
Determine the potential energy of a 0.45 kg ball being held 1.2 m above the ground.A 0.54 JB 5.29 JC 6.35 JD 0.32 J
A 4 kg vase sits on a shelf at a height of 1.2 m. How much gravitational potential energy is added to the vase when it is lifted to a shelf of height 1.4 m?A.7.84 JB.47.0 JC.54.9 JD.31.2 J
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.