A boy weighing 445 N swing on a 2-mlong swing.if his horizontal speed at the lowest point is 3m/s, what total force must the ropes holding the swing be able to withstand circular motion
To determine the total force that the ropes holding the swing must be able to withstand for circular motion, we need to consider the weight of the boy and the centripetal force acting on him at the lowest point of the swing.
The weight of the boy is given as 445 N, which is the force due to gravity acting vertically downward. Meanwhile, the centripetal force is the force required to keep the boy moving in a circular path.
At the lowest point of the swing, the gravitational force is directed downward, and the centripetal force is directed radially inward. These forces add up to provide the net force required for circular motion.
The net force in the radial direction can be calculated using the following equation:
Net force = Centripetal force + Weight
The centripetal force can be determined using the following formula:
Centripetal force = (mass × velocity^2) / radius
Given:
Weight of the boy (W) = 445 N
Radius (r) = 2 m
Velocity (v) = 3 m/s
1. First, calculate the mass of the boy using the weight formula:
Weight (W) = mass × acceleration due to gravity (g)
Rearranging the formula, we get:
Mass = Weight (W) / acceleration due to gravity (g)
Since the acceleration due to gravity is approximately 9.8 m/s^2, we have:
Mass = 445 N / 9.8 m/s^2
2. Calculate the centripetal force using the given values:
Centripetal force = (mass × velocity^2) / radius
Substitute the calculated value of the mass and given values into the equation:
Centripetal force = (mass × velocity^2) / radius
Centripetal force = (calculated mass) × (3 m/s)^2 / 2 m
3. Add the weight and centripetal force to obtain the total force:
Total force = Centripetal force + Weight
Substitute the respective values into the equation:
Total force = (calculated centripetal force) + 445 N
By following these steps and performing the necessary calculations, you can find the total force that the ropes holding the swing must be able to withstand for circular motion.