a body of mass 65kg falls freely from rest through a height of 50m find the average force exerted by the ground to bring the body to a rest
To find the average force exerted by the ground to bring the body to a rest, we can use the principle of conservation of energy.
The potential energy (PE) of the body at the initial height can be calculated using the formula:
PE = mgh
where m is the mass of the body (65 kg), g is the acceleration due to gravity (approximately 9.8 m/s^2), and h is the height (50 m).
PE = (65 kg) * (9.8 m/s^2) * (50 m)
= 31,850 J
According to the principle of conservation of energy, the potential energy at the starting point is equal to the kinetic energy (KE) at the point of coming to a rest. The kinetic energy can be calculated using the formula:
KE = (1/2) * mv^2
where m is the mass of the body (65 kg) and v is the final velocity (which is 0 m/s as the body comes to a rest).
Therefore, the kinetic energy (KE) is:
KE = (1/2) * (65 kg) * (0 m/s)^2
= 0 J
Now, the work done by the ground on the body is equal to the change in energy, which is -31,850 J (negative because the work is done against the direction of motion).
The average force exerted by the ground can be calculated using the formula:
Force = Work / Distance
In this case, the distance is the height (50 m), and the work is -31,850 J.
Force = -31,850 J / 50 m
≈ -637 N
The average force exerted by the ground to bring the body to a rest is approximately -637 Newtons. Note that the negative sign indicates that the force is exerted in the opposite direction to the motion of the body (upwards in this case).
To calculate the average force exerted by the ground to bring the body to a rest, we can use the principle of conservation of energy.
The initial gravitational potential energy (PE) of the body is given by:
PE = mgh
Where:
m = mass of the body = 65 kg
g = acceleration due to gravity = 9.8 m/s^2
h = height = 50 m
PE = (65 kg)(9.8 m/s^2)(50 m)
= 32,225 J (joules)
The final kinetic energy (KE) of the body is zero since it comes to rest.
Using the principle of conservation of energy, we can equate the initial potential energy to the final kinetic energy:
PE = KE
32,225 J = (1/2)mv^2
Since the final kinetic energy is zero, the velocity (v) of the body can be found:
0 = (1/2)mv^2
0 = (1/2)(65 kg)v^2
Solving for v, we get:
v^2 = 0
v = 0 m/s
Therefore, the body comes to rest, as expected.
Now, to find the average force exerted by the ground, we can use Newton's second law of motion:
F = ma
Since the body comes to rest, the acceleration (a) is also zero.
F = (65 kg)(0 m/s^2)
F = 0 N
Hence, the average force exerted by the ground to bring the body to a rest is 0 N.