A 66.7 kg cart is moving at 11.9 m/s around a horizontal curve whose radius is 30.5 m. What is the magnitude of the fictional force required to keep the cart from sliding?
frictionforce=mg*mu
cetnripetal disruptive force=mv^2/r
set them equal, solve for mu.
To find the magnitude of the fictional force required to keep the cart from sliding, we need to consider the centripetal force acting on the cart.
The centripetal force is the inward force that keeps an object moving in a curved path. In this case, the frictional force between the cart's wheels and the surface provides the necessary centripetal force.
The centripetal force can be calculated using the following formula:
F_c = m * v^2 / r
where F_c is the centripetal force, m is the mass of the cart, v is the velocity, and r is the radius of the curve.
Now let's substitute the given values into the formula:
m = 66.7 kg
v = 11.9 m/s
r = 30.5 m
F_c = (66.7 kg) * (11.9 m/s)^2 / 30.5 m
F_c = 9330.2923 N
Therefore, the magnitude of the fictional force required to keep the cart from sliding is approximately 9330.3 N.