The 67 kg man in the roller coaster car is sitting on a bathroom scale. If he is traveling at 33.4 m/s at the point shown and the radius of the vertical coaster track is 73 meters, to the nearest newton what does the scale read?
To determine the reading on the bathroom scale, we need to find the net force acting on the man. At this point, there are two forces acting on the man: his weight (gravitational force) and the normal force exerted by the scale.
We can start by calculating the weight of the man using the formula:
weight = mass * acceleration due to gravity
Given that the mass of the man is 67 kg and the acceleration due to gravity is approximately 9.8 m/s², we can find his weight:
weight = 67 kg * 9.8 m/s² = 656.6 N
Next, let's consider the forces acting on the man when he is on the roller coaster track. At the topmost point of the roller coaster loop (shown in the question), the normal force provided by the scale will be equal to the difference between the weight of the man and the centripetal force.
The centripetal force can be calculated using the formula:
centripetal force = (mass * velocity²) / radius
where the mass of the man is 67 kg, the velocity is 33.4 m/s, and the radius of the track is 73 meters.
centripetal force = (67 kg * (33.4 m/s)²) / 73 m
Now we can subtract the centripetal force from the weight to find the reading on the bathroom scale:
reading on the scale = weight - centripetal force
Plug in the values and calculate to find the answer to the nearest newton.