A body of net mass 200kg moving with a speed of 20m/s requires a force of 60N to maintain its circular path. calculate the radius of the path
To maintain a circular path, a centripetal force must be applied. The formula for centripetal force is:
F = (m * v^2) / r
Where F is the centripetal force, m is the mass of the object, v is the velocity, and r is the radius of the path.
In this case, we are given the mass (m = 200kg), the speed (v = 20m/s), and the force (F = 60N). Plugging these values into the formula, we can solve for the radius (r):
60N = (200kg * (20m/s)^2) / r
To solve for r, first calculate v^2:
v^2 = 20m/s * 20m/s = 400m^2/s^2
Then solve for r:
60N = (200kg * 400m^2/s^2) / r
Multiply both sides by r:
60N * r = 200kg * 400m^2/s^2
Divide both sides by 60N:
r = (200kg * 400m^2/s^2) / 60N
Simplify:
r = (80000kg·m^2/s^2) / 60N
r ≈ 1333.33 meters
Therefore, the radius of the path is approximately 1333.33 meters.
To calculate the radius of the circular path, we can use the formula for centripetal force:
Force (F) = (mass (m) * velocity (v)^2) / radius (r)
Given:
Mass (m) = 200 kg
Velocity (v) = 20 m/s
Force (F) = 60 N
Substituting these values into the formula, we have:
60 N = (200 kg * (20 m/s)^2) / r
Now, let's solve for the radius (r):
Multiply both sides of the equation by r:
60 N * r = 200 kg * (20 m/s)^2
Divide both sides of the equation by 60 N:
r = (200 kg * (20 m/s)^2) / 60 N
Calculate the value:
r = (200 kg * 400 m^2/s^2) / 60 N
r = 13,333.33 m^2/s^2 / N
Therefore, the radius of the circular path is approximately 13,333.33 meters.