A full shopping cart requires a force of 88.0 Newtons to move across a horizontal floor at a constant velocity. If the cart has a mass of 32.1 kg, what is the coefficient of kinetic friction between the cart and the floor?
mu m g = 88 = m g
mu = 88/(32.1*9.81)
To find the coefficient of kinetic friction between the cart and the floor, we can use the following formula:
frictional force (Ff) = coefficient of kinetic friction (μk) × normal force (Fn)
In this case, the normal force is equal to the weight of the cart, which is given by:
Fn = mass × gravitational acceleration
Fn = 32.1 kg × 9.8 m/s^2
Now that we know the normal force, we can rearrange the formula to find the coefficient of kinetic friction:
μk = Ff / Fn
To find the frictional force, we need to use the fact that the cart is moving at a constant velocity. This means that the force applied to overcome the friction is equal to the frictional force:
Ff = 88.0 N
Now we can substitute the values into the formula:
μk = 88.0 N / (32.1 kg × 9.8 m/s^2)
Calculating the value will give us the coefficient of kinetic friction between the cart and the floor.