a stone of mass o.5 kg is dropped from a height of 5om.what is the kinetic energy of the stone just before it strikes the ground?
The KE at the bottom will equal the original Potential energy at the start.
KE=PE
KE=mass*g*heightinmeters
To determine the kinetic energy of the stone just before it strikes the ground, you can use the formula for kinetic energy:
Kinetic energy (KE) = (1/2) * mass * velocity^2
First, we need to calculate the velocity of the stone just before it strikes the ground. To do that, we can use the equations of motion. Considering the stone is dropped from rest with no initial velocity, we can use the equation for vertical displacement:
Displacement (s) = ut + (1/2) * acceleration * t^2
Where:
- u is the initial velocity (which is 0 in this case)
- t is the time taken to fall (unknown)
- acceleration (a) is the acceleration due to gravity, approximately 9.8 m/s^2
- s is the displacement or height (50 m)
Rearranging the equation, we have:
s = (1/2) * a * t^2
Substituting the given values, we solve for t:
50 = (1/2) * 9.8 * t^2
100 = 9.8 * t^2
t^2 = 100 / 9.8
t^2 ≈ 10.2041
t ≈ √10.2041
t ≈ 3.19 seconds (rounded to two decimal places)
Now that we know the time taken to fall is approximately 3.19 seconds, we can calculate the velocity using the equation:
Velocity (v) = initial velocity + acceleration * time
Since the stone is dropped from rest, the initial velocity is 0 m/s:
v = 0 + 9.8 * 3.19
v ≈ 31.202 m/s (rounded to three decimal places)
Finally, we can substitute the mass (0.5 kg) and velocity (31.202 m/s) into the formula for kinetic energy to find the answer:
KE = (1/2) * mass * velocity^2
KE = (1/2) * 0.5 * (31.202)^2
KE ≈ 243.840 Joules (rounded to three decimal places)
Therefore, the kinetic energy of the stone just before it strikes the ground is approximately 243.840 Joules.