A small boy of mass 0.2kg moves uniformly in a circle on a horizontal frictionless surface, attached by a cord 0.2m long to a pin set in the surface. If the body makes two complete revolutions per second, find the force P exterted on it by the cord.
The speed of the boy is
V = 2* 2 pi R per second
Compute that and then compute the centripetal force
F = M V^2/R
M is the mass and R is the radius of the cord.
To find the force exerted on the small boy by the cord, we need to compute the centripetal force acting on the body. The centripetal force is the force that keeps an object moving in a circular path.
First, let's find the speed of the boy. We are given that the boy makes two complete revolutions per second.
One complete revolution is when the boy travels around the entire circumference of the circle. The circumference of a circle is given by 2πR, where R is the radius of the circle.
In this case, the length of the cord is given as 0.2m, which is equal to the radius of the circle (R = 0.2m).
To find the speed, we need to multiply the distance traveled per revolution (which is the circumference of the circle) by the number of revolutions per second.
Speed (V) = 2 * 2πR = 2 * 2π * 0.2m
Now that we have the speed (V) of the boy, we can compute the centripetal force (F).
The centripetal force (F) is given by the formula:
F = M * V^2 / R
Where M is the mass of the boy and R is the radius of the circle.
In this case, the mass of the boy (M) is given as 0.2kg, and the radius of the circle (R) is given as 0.2m.
Substituting the values into the formula, we can calculate the centripetal force:
F = 0.2kg * (2 * 2π * 0.2m)^2 / 0.2m
Simplifying the equation:
F = 0.2kg * (4π * 0.2m)^2 / 0.2m
F = 0.2kg * (4π * 0.2m * 4π * 0.2m)
F = 0.2kg * (16π^2 * 0.04m^2)
F = 0.128π^2 kg * m^2
F ≈ 1.278 N
Therefore, the force exerted on the small boy by the cord is approximately 1.278 Newtons (N).