a 70 kg cart on a roller coaster has a motor that keeps it moving at constant speed in a circular, vertical loop whose radius is 14 meters. At point A, the centripetal force on the cart is 1000 N. The cart has wheels on both sides of the track so that it cannot leave leave track.
The amount of force exerted on the cart by the track at the top is approximately
a) 300 N
b) 700 N
c) 1700 N
d) 1300 N
e) 0 N
would it be 1700 because the force of gravity and the normal force are acting on it?
To determine the force exerted on the cart by the track at the top of the loop, we need to consider the forces acting on the cart at that point.
At the top of the loop, the cart experiences two main forces: the force of gravity acting downwards and the normal force exerted by the track upwards.
The centripetal force required to keep the cart moving in a circular path is provided by the net force acting towards the center of the loop. In this case, the net force is the difference between the normal force and the force of gravity.
Given that the centripetal force is 1000 N, we can set up the following equation:
Centripetal force = Normal force - Force of gravity
1000 N = Normal force - m*g
where m is the mass (70 kg) and g is the acceleration due to gravity (approximately 9.8 m/s²).
Considering the value of g and rearranging the equation, we can solve for the normal force:
Normal force = 1000 N + m*g
Normal force = 1000 N + (70 kg)(9.8 m/s²)
Calculating this, we get:
Normal force ≈ 1000 N + 686 N
Normal force ≈ 1686 N
Therefore, the approximate force exerted on the cart by the track at the top of the loop is 1686 N. Since none of the given options match this value exactly, we can conclude that the closest answer is (c) 1700 N.