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You're driving home from the grocery store at 18 m/s with a 7. 0 kg bag of groceries on the front seat when the light ahead turns red. What is the shortest distance in which you can stop, after the brakes are applied, without the groceries sliding off the seat? the static and kinetic coefficients of friction are, respectively, 0. 65 and 0. 45. Assume that the surface of the seat is horizontal



Answer :

ayune

The minimum distance such that the grocery bag does not slide off when the brake force applied is 25.43 m

The grocery bag will start to slide off if the force exerted by the brake is equal to the maximum static friction force.

Let:

Fs = static friction force

F = force exerted by the brake

m = mass of the grocery bag

v = velocity

μs = static coefficients of friction

g = gravitational acceleration = 9.8 m/s²

Then,

Fs = - μs . m. g

F = m . a

Fs = F

- μs . m. g = m . a

a = μs .  g = 0.65 . 9.8 = - 6.37 m/s²

With this deceleration, the distance (s) will be:

v² = u² + 2 . a. s

Where v = 0 (since vehicle stops), u = 18 m/s

0 = 18² + 2 . (- 6.37 ) . s

s = 25.43 m

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