sapling learning At a mail sorting facility, packages slide down a ramp but are

Question

sapling learning At a mail sorting facility, packages slide down a ramp but are stopped part way down the ramp so that they can be scanned. While the packages are scanned, they are held in place by a horizontal force from a spring-loaded arm. Calculate the force that must be applied by this arm to hold a package on the ramp. The ramp is at an angle of 41.5° with the horizontal. The package has a mass of 2.25 kg. The coefficient of static friction between the ramp and the package is 0.435 Number 41.5 o

Explanation / Answer

The force pulling the package down Fw = m*g*sin

The component of the spring force in the direction of the ramp is Fs = Fa*cos.

Fn is the net normal force of the package against the ramp: Fn = m*g*cos + Fa*sin;

Before the package starts to move, this force will be aided by the frictional force, which is Fr = u*Fn

Fr = u*(m*g*cos + Fa*sin)

For the package to slide, the weight must at least equal the applied force component and overcome the friction force:

m*g*sin = Fa*cos + u*(m*g*cos + Fa*sin)
Fa*(cos + u*sin) = m*g*(sin - u*cos)
Fa = m*g*(sin - u*cos)/(cos + u*sin)

Fa = 2.25*9.8*(sin 41.5 - 0.435*cos41.5)/(cos 41.5 + 0.435*sin 41.5)

Fa = 7.16 N

if you find any question marks in the answer then assoume them 'theta'

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