A 0.135 kg ball is dropped from rest. If the magnitude of the ball's momentum is 0.730 kg·m/s just before it lands on the ground, from what height was it dropped?
A ball with a mass 100g is dropped from a height of 20m it's a volicty at4 m how??
A ball with a mass 100g is dropped from a height of 20m it's a volicty at4 m how??
To find the height from which the ball was dropped, you can use the principle of conservation of mechanical energy. The ball is dropped from rest, so it has an initial potential energy (PE) that will be converted to kinetic energy (KE) just before it lands. Assuming no other forces are acting on the ball (such as air resistance), the total mechanical energy remains constant.
The total mechanical energy is the sum of the potential energy and the kinetic energy:
Total mechanical energy = Potential energy (PE) + Kinetic energy (KE)
At the maximum height (when the ball is dropped), all the initial energy is potential energy because the ball is at rest. Therefore, the initial potential energy (PE) is equal to the total mechanical energy:
PE = Total mechanical energy
When the ball is just about to land, all the energy is in the form of kinetic energy. Therefore, the final kinetic energy (KE) is equal to the total mechanical energy:
KE = Total mechanical energy
The potential energy is given by the formula:
Potential energy (PE) = mass (m) * gravity (g) * height (h)
where:
mass (m) = 0.135 kg (given)
gravity (g) = 9.8 m/s^2 (acceleration due to gravity, approximately)
The kinetic energy is given by the formula:
Kinetic energy (KE) = 0.5 * mass (m) * velocity squared (v^2)
where:
mass (m) = 0.135 kg (given)
velocity (v) = 0.730 kg·m/s (given)
Now, we have the formulas for potential energy and kinetic energy. Equating them to the total mechanical energy, we can solve for the height:
PE = KE
m * g * h = 0.5 * m * v^2
Canceling out the mass (m) on both sides:
g * h = 0.5 * v^2
Substituting the given values:
9.8 * h = 0.5 * (0.730)^2
Simplifying the equation:
9.8 * h = 0.5 * 0.5329
9.8 * h = 0.26645
Dividing both sides by 9.8:
h = 0.26645 / 9.8
Calculating the result:
h ≈ 0.0272 meters
Therefore, the ball was dropped from a height of approximately 0.0272 meters.