A boy weighing 445 N swings on a 2-m long swing. If his horizontal speed at the lowest point is 3 m/s, what total force must the ropes holding the swing be able to withstand?
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To determine the total force the ropes holding the swing must be able to withstand, we need to consider the forces acting on the boy at the lowest point of the swing.
At the lowest point of the swing, the boy is experiencing two forces: the force of gravity pulling him downward and the force of tension in the ropes pulling him inward.
The force of gravity acting on the boy is equal to his weight, which is given as 445 N.
The tension in the ropes is responsible for providing the centripetal force required to keep the boy moving in a circular path. Since the swing is moving horizontally at the lowest point, the centripetal force is provided solely by the tension in the ropes.
Using the centripetal force equation, we can calculate the tension in the ropes:
Centripetal force = Mass × (Horizontal velocity)^2 / Radius
The mass of the boy is not given directly, but we can calculate it using the weight and the acceleration due to gravity. The formula to calculate weight is:
Weight = Mass × Acceleration due to gravity
Therefore, we can rearrange the equation to solve for mass:
Mass = Weight / Acceleration due to gravity
The acceleration due to gravity is approximately 9.8 m/s^2.
Let's substitute the given values into the equation...
Mass = 445 N / 9.8 m/s^2
Calculating this gives the mass of the boy.
Once we have the mass, we can substitute it, along with the horizontal velocity and radius, into the centripetal force equation to calculate the tension in the ropes.
Finally, the total force the ropes must be able to withstand is equal to the sum of the gravitational force and the tension in the ropes.