apling learning Map t a mail sorting facility, packages slide down a ramp but ar

Question

apling learning Map t a mail sorting facility, packages slide down a ramp but are stopped part way down the ramp so that they can be scanned. Whi spring-loaded arm. Calculate the minimum force that must be applied by this arm to hold a ramp. The ramp is at an angle of 29.5° with the horizontal. The package has a mass of 4.75 kg. T coefficient of static friction between the ramp and the package is 0.43 ile the packages are scanned, they are held in place by a horizontal force from a on the Number 4.794 29.5 There is a hint available! View the hint by clicking on the bottom divider bar. Click on the divider bar again to hide the hint. Close O Previous Check Answer Next Exit

Explanation / Answer

The weight acts downward

Fw = m*g*sin

The component of the spring force in the direction of the ramp:

Fs = Fa*cos.

Frictional force acts before it move

Fr = µ*Fn

Here Fn is the net normal force of the package against the ramp:

Fn = m*g*cos + Fa*sin;

Therefore, the frictional force

Fr = µ*(m*g*cos + Fa*sin)

In the case of the package to slide, the weight must at least equal

the applied force component and overcome the friction force.

m*g*sin = Fa*cos + µ*(m*g*cos + Fa*sin)

Solve the equtaion for Fa

Fa = m*g*(sin - µ*cos)/(cos + µ*sin)

Substitute given values

Fa = ( 4.75 ) ( 9.81 ) (sin 29.5 - (0.435 ) cos 29.5 ) / (cos 29.5 + (0.435 ) sin29.5)

Fa = 4.88 N

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