driving in a car with constant speed of 12m/s,then encounter to a bump that has a circular cross-section and a radius of 35m.find the apparent weight of a 70 kg person in the car over the top of bump
ma=mg-N
W=N=m(g-a)=m [g- (v²/R)]
To find the apparent weight of a person in the car while going over the top of a bump, we can start by understanding the forces acting on the person.
When the car goes over the top of the bump, the person will experience both gravitational force and a normal force.
The weight of the person is given by the formula:
Weight = mass * acceleration due to gravity
In this case, the mass of the person is 70 kg, and the acceleration due to gravity is approximately 9.8 m/s^2.
Weight = 70 kg * 9.8 m/s^2
= 686 N
Now let's consider the forces acting on the person when going over the top of the bump. At the top of the bump, the normal force acting on the person will be equal to the sum of the gravitational force and the centripetal force.
The centripetal force is given by the formula:
Centripetal force = mass * velocity^2 / radius
In this case, the mass is 70 kg, the velocity is constant at 12 m/s, and the radius of the bump is 35 m.
Centripetal force = (70 kg * (12 m/s)^2) / 35 m
= 345.6 N
The normal force is the apparent weight of the person, so the apparent weight of the person at the top of the bump is:
Apparent weight = Weight + Centripetal force
= 686 N + 345.6 N
= 1031.6 N
Therefore, the apparent weight of the 70 kg person in the car over the top of the bump is approximately 1031.6 N.