The student claims that a ball dropped 3.0 meters would have fewer than 96 joules of kinetic energy upon hitting the ground. Is she correct? Why?
To determine if the student's claim is correct, we need to use the formula for kinetic energy:
Kinetic Energy = 0.5 * mass * velocity^2
We don't have the mass of the ball or its velocity, so we cannot calculate the exact kinetic energy. However, we can analyze the claim using the concept of potential energy.
When the ball is dropped from a height of 3.0 meters, it will convert its potential energy to kinetic energy as it falls.
Potential Energy = mass * gravitational acceleration * height
Since the ball is only dropped, its initial velocity is zero. Thus, all of the potential energy is converted to kinetic energy.
So, if the ball were dropped from a height of 3.0 meters, the potential energy at that height would be converted to kinetic energy upon hitting the ground.
Therefore, the student's claim is incorrect. The kinetic energy upon hitting the ground would be equal to the potential energy at the height of 3.0 meters, which in turn would depend on the mass of the ball.
To determine whether the student's claim is correct, we need to calculate the kinetic energy of the ball when it hits the ground.
The formula for calculating kinetic energy is:
Kinetic Energy (KE) = 1/2 * mass * velocity^2
In this case, we don't have the mass or velocity of the ball, but we can use the principle of conservation of energy to find the velocity.
When the ball is dropped, it converts its potential energy (mgh) into kinetic energy (KE), where m is the mass of the ball, g is the acceleration due to gravity (approximately 9.8 m/s^2), and h is the height from which the ball is dropped.
Since the ball is dropped from a height of 3.0 meters in this case, the potential energy is given by:
Potential Energy (PE) = m * g * h
We can equate the potential energy to the kinetic energy:
Potential Energy (PE) = Kinetic Energy (KE)
m * g * h = 1/2 * m * v^2
Where v is the velocity of the ball.
Simplifying the equation:
m * g * h = 1/2 * m * v^2
Now we can cancel out the mass (m) on both sides of the equation:
g * h = 1/2 * v^2
Next, we isolate v^2 by multiplying both sides by 2:
2 * g * h = v^2
Finally, we take the square root of both sides to find the velocity:
v = √(2 * g * h)
Now we can substitute the given values into the equation:
v = √(2 * 9.8 m/s^2 * 3.0 m)
v = √(58.8 m^2/s^2)
v ≈ 7.67 m/s
Now that we have the velocity, we can calculate the kinetic energy:
KE = 1/2 * m * v^2
However, we still don't know the mass of the ball, so we cannot calculate the exact kinetic energy. Therefore, we cannot determine whether the student's claim is correct or not without knowing the mass of the ball.