a 57.0 kg person in a rollercoaster moving through the bottom of a curved track of radius 42.7 m feels a normal force of 995 N. How fast is the car moving?
Please help quickly it!!!
To find the speed at which the car is moving, we can use the concept of centripetal force.
First, we need to find the net force acting on the person. At the bottom of a curved track, the net force consists of the force of gravity (mg) and the normal force (N). So, the net force (F_net) is given by:
F_net = mg + N
In this case, the mass of the person (m) is given as 57.0 kg, and the normal force (N) is given as 995 N.
Substituting these values into the formula, we get:
F_net = (57.0 kg)(9.8 m/s^2) + 995 N
Next, we can relate the net force to the centripetal force (F_c) using the equation:
F_c = (m)(v^2)/r
Here, v is the velocity or speed of the car, and r is the radius of the curved track.
Since the centripetal force is equal to the net force, we can equate the two equations:
F_net = F_c
So, we can write:
(m)(v^2)/r = (57.0 kg)(9.8 m/s^2) + 995 N
We know the mass (m) is 57.0 kg, and the radius (r) is given as 42.7 m.
Now, let's substitute these values into the equation:
(57.0 kg)(v^2)/42.7 m = (57.0 kg)(9.8 m/s^2) + 995 N
Next, simplify the equation by canceling out the mass:
(v^2)/42.7 m = 9.8 m/s^2 + (995 N)/(57.0 kg)
Now, multiply both sides of the equation by 42.7 m:
v^2 = (42.7 m)(9.8 m/s^2 + (995 N)/(57.0 kg))
Finally, take the square root of both sides to solve for v, the velocity/speed:
v = √[(42.7 m)(9.8 m/s^2 + (995 N)/(57.0 kg))]
Calculating this expression will give you the speed at which the car is moving.
gravity + centripetal = normal ... (m * g) + (m * v^2 / r) = 995 N
solve for v