At what height above the ground must a body of mass 10kg be situated in order to have potential energy equal in value to the kinetic energy possessed by another body of mass 10kg moving with a velocity of 10ms-1 ?
(1/2) m v^2 = m g h
h = v^2/(2g)
home work
at what height above the ground must a body of mass 10kg be situated in order to have a potential energy equal in value to the kinetic energy possessed by another body of mass 10kg moving with a velocity of 10m/s?(take g=10m/s)
ilike to solve me my physics assignment.
To determine the height above the ground at which a 10kg body must be situated in order to have potential energy equal to the kinetic energy of another 10kg body moving at 10 m/s, we can use the principle of conservation of energy.
1. Firstly, we need to find the kinetic energy possessed by the moving body using the formula:
Kinetic Energy (KE) = 1/2 * mass * velocity^2.
For the given body with a mass of 10kg and velocity of 10 m/s:
KE = 1/2 * 10 kg * (10 m/s)^2
= 1/2 * 10 * 100
= 500 Joules.
2. According to the conservation of energy, this kinetic energy should be equal to the potential energy of the elevated body. The potential energy (PE) of an object at a certain height can be calculated using the formula:
Potential Energy (PE) = mass * gravity * height.
Here, the mass is 10kg and the gravity can be considered as 9.8 m/s^2 (approximate value on Earth).
Therefore, we have:
PE = 10 kg * 9.8 m/s^2 * height
3. Since the potential energy is equal to the kinetic energy (PE = KE), we can equate the two expressions and solve for the height:
10 kg * 9.8 m/s^2 * height = 500 J
4. Solving for the height:
height = 500 J / (10 kg * 9.8 m/s^2)
= 5.1 meters (rounded to one decimal place).
Therefore, the body of mass 10kg must be situated at a height of approximately 5.1 meters above the ground in order to have potential energy equal to the kinetic energy possessed by the moving body of the same mass.