A 16kg stone falls 40m. Find the stone's kinetic energy just before it strikes the ground.
velocity when stone hits the ground
v = √2as
KE = 1/2 mv^2 = 1/2 m * 2as = m*a*s
= 16 * 9.8 * 40 = 6272kg-m/s^2(N)
To find the stone's kinetic energy just before it strikes the ground, we can use the formula for kinetic energy:
Kinetic Energy (K.E.) = (1/2) * mass * velocity^2
In this case, we are given the mass of the stone, which is 16 kg. However, we need to find the velocity at which it falls before we can calculate the kinetic energy.
To find the velocity of the stone just before it strikes the ground, we can use the equation of motion for uniformly accelerated motion:
v^2 = u^2 + 2aS
Where:
v = final velocity
u = initial velocity (which is 0 in this case since the stone starts from rest)
a = acceleration due to gravity (-9.8 m/s^2, assuming downward direction)
S = distance fallen by the stone (40 m in this case)
Plugging in the values, we can solve for v:
v^2 = 0^2 + 2 * (-9.8 m/s^2) * 40 m
v^2 = 0 + (-784) m^2/s^2
v^2 = -784 m^2/s^2
Since we're dealing with magnitudes, we take the positive square root:
v = 28 m/s
Now that we have the velocity, we can calculate the stone's kinetic energy just before it strikes the ground:
K.E. = (1/2) * mass * velocity^2
K.E. = (1/2) * 16 kg * (28 m/s)^2
K.E. = (1/2) * 16 kg * 784 m^2/s^2
K.E. = 6272 J
Therefore, the stone's kinetic energy just before it strikes the ground is 6272 joules.