Dynamics University Level Physics/Mechanical Engineering Problem As shown below,

Question

Dynamics University Level Physics/Mechanical Engineering Problem

As shown below, a 10-lb package A is moving with conveyor belt B at a constant velocity. Package A leaves belt B and lands on another 40-lb belt C which is initially at rest but is free to move horizontally. Immediately after landing on belt C package A has a horizontal velocity of 20 ft/s and belt C has zero velocity. Determine the time and the distance that package A travels before it stops sliding relative to belt C. The coefficient of kinetic friction in all surfaces is mu_k = 0.4 .

Explanation / Answer

here,

weight of package , w = 10 lb

initial speed , u = 20 ft/s

u = 6.096 m/s

uk = 0.4

accelration due friction , a = - uk * g

a = - 3.92 m/s^2

let the distance travelled be s

using third equation of motion

v^2 - u^2 = 2 * a * s

0 - 6.096^2 = - 2 * 3.92 * s

s = 4.74 m

the distance travelled is 4.74 m

let the time taken be t

v = u + a * t

0 = 6.096 - 3.92 * t

t = 1.56 s

the time taken is 1.56 s

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