A body of mass 2kg is released from rest and falls
freely under gravity. Find its speed when it has
fallen a distance of 10m.
To find the speed of the body when it has fallen a distance of 10m, we can use the equation for gravitational potential energy:
Potential energy (PE) = mgh
Where:
m = mass of the body (2kg)
g = acceleration due to gravity (9.8 m/s^2)
h = height fallen (10m)
Since the body is released from rest, all its initial potential energy is converted into kinetic energy as it falls:
PE = KE
Therefore, we can set up the equation:
mgh = (1/2)mv^2
Where:
v = speed of the body
Simplifying the equation:
2 * 9.8 * 10 = (1/2) * 2 * v^2
196 = v^2
Taking the square root of both sides:
v = √196
v = 14 m/s
Therefore, the speed of the body when it has fallen a distance of 10m is 14 m/s.
To find the speed of the body when it has fallen a distance of 10m, we can use the equation for gravitational potential energy.
The gravitational potential energy (PE) of an object near the Earth's surface can be calculated using the formula:
PE = m * g * h
Where:
m = mass of the body = 2kg
g = acceleration due to gravity = 9.8 m/s^2
h = height fallen = 10m
So, the potential energy at a height of 10m is given by:
PE = 2kg * 9.8 m/s^2 * 10m = 196 Joules
The potential energy is converted to kinetic energy as the object falls. Therefore, at a height of 10m, all of the potential energy will be converted to kinetic energy. The equation for kinetic energy is given by:
KE = 0.5 * m * v^2
Where:
m = mass of the body = 2kg
v = velocity of the body (speed)
Since the potential energy is converted entirely to kinetic energy, we can set PE equal to KE:
PE = KE
So, 196 Joules = 0.5 * 2kg * v^2
Rearranging the equation, we can solve for v:
v^2 = (2 * PE) / m
v = sqrt((2 * 196 Joules) / 2kg)
v = sqrt(392 Joules/kg)
Calculating this value:
v ≈ 19.8 m/s
Therefore, the speed of the body when it has fallen a distance of 10m is approximately 19.8 m/s.