(10%) Problem 6: Abox of mass m = 0.38 kg is set against a spring with a spring

Question

(10%) Problem 6: Abox of mass m = 0.38 kg is set against a spring with a spring constant of k1 526 N/m which has been compressed by a distance of 0.1 m. Some distance in front of it, along a frictionless surface, is another spring with a spring constant of k2=112Nm. Otheexpertta.com 33% Part (a) How far, d2 in meters, will the second spring compress when the box runs into it? Grade Summary Potential 100% cotanO asinacosO atan0 acotanO sinh0 cosh tanh (0% per attempt) detailed view °Degrees Radians Subenit Hint Hints: 0% deduction per hint. Hints remaining: Feedback: deduction per feedback. 33% Part(b) How fast, v in meters per second, will the box be moving when it strikes the second spring? i 33% Part (c) Now assume that the surface is rough (that is, not frictionless). You perform the experiment and observe that the second spring only compresses a distance d2. How much energy, in joules, was lost to friction?

Explanation / Answer

compress distance for spring1 = 0.1 m

so potential energy of spring = (1/2)kx^2 = 0.5*526*(0.1)^2 = 2.63 J

the surface is frictionless so energy wil transfer to second spring and compress distance for spring1 is d2

so 2.63 = 0.5*k2*d2^2

d2^2 = 2.63/(0.5*112)

d2 = 0.217 m

b)

box is moving with speed v when it strikes the second spring so

2.63 = (1/2)mv^2

v = sqrt(2.63*2/0.38) = 3.72 m/s

c)

if second spring only compresses a distance d2/2 then energy lose

energy lost = 2.63 - 0.5*112*(0.217/2)^2 = 1.97 Joules

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