A 3.6 -kg mass attached to the end of a string swings in a vertical circle (radius = 17.9 m). When the string is horizontal, the speed of the mass is 3.8 m/s. What is the magnitude of
the force of the string on the mass at this position?
m g
To find the magnitude of the force of the string on the mass when the string is horizontal, we can use the concept of centripetal force.
The centripetal force is the force that keeps an object moving in a circular path. In this case, when the string is horizontal, the tension in the string provides the centripetal force for the mass.
The centripetal force can be calculated using the formula:
F = (m * v^2) / r
where F is the centripetal force, m is the mass of the object, v is the velocity of the object, and r is the radius of the circular path.
Given:
Mass (m) = 3.6 kg
Velocity (v) = 3.8 m/s
Radius (r) = 17.9 m
Substituting the given values into the formula, we get:
F = (3.6 kg * (3.8 m/s)^2) / 17.9 m
Calculating this expression will give us the magnitude of the force of the string on the mass.
F = (3.6 kg * 14.44 m^2/s^2) / 17.9 m
F = 51.984 kg m/s^2 / 17.9 m
F ≈ 2.905 kg m/s^2
Therefore, the magnitude of the force of the string on the mass when the string is horizontal is approximately 2.905 kg m/s^2.