A stick of length 1.2 m is held vertically with one end on the floor and is then allowed to fall. Find the speed of the other end when it hits the floor, assuming that the end on the floor does not slip.
To find the speed of the other end of the stick when it hits the floor, we can use the principle of conservation of energy. This principle states that the total mechanical energy of a system remains constant if no external forces are acting on it.
In this case, as the stick falls, its potential energy is converted into kinetic energy. The potential energy when the stick is held vertically can be calculated using the equation:
Potential energy = mgh
where m is the mass of the stick, g is the acceleration due to gravity, and h is the height of the stick.
Since the stick is held vertically with one end on the floor, the height given by h is the length of the stick, which is 1.2 m.
When the other end of the stick hits the floor, all of its potential energy is converted into kinetic energy. The kinetic energy can be calculated using the equation:
Kinetic energy = 0.5mv^2
where v is the speed of the other end of the stick when it hits the floor.
According to the principle of conservation of energy, the potential energy at the initial position is equal to the kinetic energy at the final position. Therefore, we can equate the two equations:
mgh = 0.5mv^2
We can cancel out the mass (m) from both sides of the equation:
gh = 0.5v^2
To find v, we can rearrange the equation:
v^2 = 2gh
Finally, we can take the square root of both sides to find v:
v = sqrt(2gh)
Now we can substitute the known values into the equation. Assuming the acceleration due to gravity is approximately 9.8 m/s^2:
v = sqrt(2 * 9.8 * 1.2)
v ≈ 6.65 m/s
Therefore, the speed of the other end of the stick when it hits the floor is approximately 6.65 m/s.