If a person who weighs 125lb, rides a roller coaster with a 100m diameter loop at 30m/s. What force did the person exert?
To determine the force exerted by the person during the roller coaster ride, we need to analyze the different forces acting on them.
The two main forces involved are the force of gravity (weight) and the normal force. The normal force is the force exerted by a surface to support the weight of an object resting on it. In this case, the normal force is provided by the roller coaster seat, preventing the person from falling.
To calculate the force exerted by the person, we can start by calculating the gravitational force. The formula to calculate weight (gravitational force) is:
Weight = mass × acceleration due to gravity
Given that the person weighs 125 lb, we need to convert this value to kilograms since the units we will use are metric. We know that 1 lb is approximately equal to 0.4536 kg, so the person's weight in kg is approximately:
125 lb × 0.4536 kg/lb ≈ 56.7 kg
Now, we can calculate the force of gravity by using the formula:
Weight = mass × acceleration due to gravity
The acceleration due to gravity is approximately 9.8 m/s^2. Therefore:
Weight = 56.7 kg × 9.8 m/s^2
Weight = 556.86 N
Now, let's consider the motion in the loop. When the roller coaster reaches the top of the loop, the person experiences a net inward force, which is the sum of the gravitational force and the normal force. The normal force provides the centripetal force required to keep the person moving in a circular path.
The net inward force can be calculated using the formula:
Net inward force = Weight + Normal force
Since we are looking for the force exerted by the person, we need to find the normal force. At the top of the loop, the normal force is equal to the sum of the person's weight and the centripetal force required to keep them moving along the circular path.
The centripetal force can be calculated using the formula:
Centripetal force = mass × (velocity^2 / radius)
Given that the diameter of the loop is 100 m, the radius is half of that, which is 50 m.
The velocity of the person is given as 30 m/s, and the mass is already calculated as 56.7 kg.
Now, we can substitute these values into the centripetal force formula:
Centripetal force = 56.7 kg × (30 m/s)^2 / 50 m
Centripetal force = 102.06 N
Therefore, the normal force (and also the net inward force exerted by the person) is:
Net inward force = Weight + Normal force
Net inward force = 556.86 N + 102.06 N
Net inward force = 658.92 N
Hence, the force exerted by the person during the roller coaster ride is approximately 658.92 Newtons.