Problem 15.82 10 of 10> The 8-lb box slides on the surface for which H -0.3 The

Question

Problem 15.82 10 of 10> The 8-lb box slides on the surface for which H -0.3 The box has a velocity v 15 ft/s when it is 2 ft from the plate. (Figure 1) Part A If the box strikes the smooth plate, which has a weight of 24 lb and is held in position by an unstretched spring of stiffness k 270 lb/ft, determine the maximum compression imparted to the spring. Take e-0.8 between the box and the plate. Assume that the plate slides smoothl Express your answer using three significant figures and include the appropriate units Vale Units Figure 1 of 1 Submit Request Answer K Return to Assignment Provide Feedback v-15 ft/s 2 ft

Explanation / Answer

Using energy conservation,

K.E + E.P.E = K.E2    (HERE m = w/g = 8 / 32.2 = 0.248)

1/2*0.248*152 - 0.3*2*8 = 1/2*0.248*V2

V2 =  23.1 / 0.124

V = 13.65 FT/S

Then you can use conservation of momentum,

However, there is a short way to solve this problem.

we know that v2 = u2 - 2ad

so, v2 = u2 - 2*g*d*uk where uk is unitless

Fro this type of problem, we use conservation of momentum before and after collision, conservation of energy during spring compression.

using these, we have a standard formula

x = 1+e / 1 + w/W (sqrt (m/k(u2 - 2*g*d*uk )

where w - 24 , W - 8 , m - 24/32.2 = 0.7453

Putting all the given values, we have

x = 1+0.8 / 4 sqrt (0.00276 (213.24))

x = 1+0.8 / 4 *0.767165

x = 0.3452 m

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