Six roller-coaster carts pass over the same semicircular "bump." The mass M of each cart (including passenger) and the normal force n of the track on the cart at the top of each bump are given in the figures.
Iam given the force in N of the cart at the peak of the loop and the mass of each cart.
How do i find the velocity of the carts?
To find the velocity of the carts, you can use the principle of conservation of mechanical energy. The mechanical energy of a system is the sum of its kinetic energy and potential energy.
In this case, at the peak of the loop, all of the potential energy of the carts is converted into kinetic energy. We can set the potential energy at the bottom of the loop to zero, so the potential energy at the top of the loop is Mgh, where M is the mass of the cart (including passenger), g is the acceleration due to gravity, and h is the height of the bump.
The kinetic energy of the carts at the top of the loop is given by (1/2)MV^2, where V is the velocity of the carts.
According to the principle of conservation of mechanical energy, the sum of the potential and kinetic energy at the top of the loop should be equal to the potential energy at the bottom of the loop (which is zero). Therefore, we can set up the following equation:
Mgh = (1/2)MV^2
We can cancel out the mass M from both sides of the equation, giving:
gh = (1/2)V^2
Solving for V, we get:
V = √(2gh)
Substituting the given values of g and h, you can calculate the velocity V of the carts.