an object has a potential energy of 100 J when it is 10 m above the ground. if it were to fall without friction what would its kinetic energy be the instant it hits the ground
Follow the rule of conservation of energy.
To calculate the kinetic energy of the object the instant it hits the ground, we need to understand the law of conservation of energy. The total mechanical energy of the object is conserved, meaning that the sum of its potential energy and kinetic energy remains constant.
Given that the object has a potential energy of 100 J when it is 10 m above the ground, we can express this as:
Potential Energy = 100 J
Height = 10 m
The formula for gravitational potential energy (PE) is:
PE = m * g * h
where m is the mass of the object, g is the acceleration due to gravity (9.8 m/s²), and h is the height.
To find the mass of the object, we need more information. If the mass of the object is given, we can proceed with the calculation. Let's assume the mass of the object is 1 kg.
PE = m * g * h
100 J = 1 kg * 9.8 m/s² * 10 m
Now, let's solve for the mass:
m = 100 J / (9.8 m/s² * 10 m)
m = 1 kg
Since the potential energy is equal to the kinetic energy when the object hits the ground (assuming all of the potential energy is converted into kinetic energy), we can equate the two:
Potential Energy = Kinetic Energy
100 J = (1/2) * m * v²
Now, solve for the velocity (v):
v² = (2 * 100 J) / m
v² = (2 * 100 J) / 1 kg
v² = 200 J/kg
v = sqrt(200 J/kg)
v ≈ 14.14 m/s
Therefore, the kinetic energy of the object when it hits the ground would be approximately 100 J.