Question 19 of 24 Map Sapling Learning macmillan learning At a mail sorting faci

Question

Question 19 of 24 Map Sapling Learning macmillan 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 minimum force that must be applied by this arm to hold a package on the ramp. The ramp is at an angle of 43.5° with the horizontal. The package has a mass of 3.25 kg. The coefficient of static friction between the ramp and the package is 0.435 Number 43.5°

Explanation / Answer

here,

mass , m = 3.25 kg

us = 0.435

theta = 43.5 degree

let the minimum force applied be F

normal force , N = m * g* cos(theta) + F * sin(theta)

for the block to not move

accelration , a = 0

(Fcos(theta) + us * N - m * g * sin(theta)) = 0

( F * cos(43.5)) + 0.435 * (3.25 * 9.81* cos(43.5) + F * sin(43.5) - 3.25 * 9.81 * sin(43.5) = 0

solving for F

F = 11.6 N

the minimum force required is 11.6 N

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