(8.9)Please help with number 9 and show your work. Thanks. A light spring of for
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(8.9)Please help with number 9 and show your work. Thanks.
A light spring of force constant 4.05 N/m is compressed by 8.00 cm and held between a 0.250 kg block on the left and a 0.600 kg block on the right. Both blocks are at rest on a horizontal surface. The blocks are released simultaneously so that the spring tends to push them apart. Find the maximum velocity each block attains if the coefficient of kinetic friction between each block and the surface is the following. In each case, assume that the coefficient of static friction is greater than the coefficient of kinetic friction. Let the positive direction point to the right. Your response differs from the correct answer by more than 10%. Double check your calculations, m/s your response is within 10% of the correct value. This may be due to roundoff error, or you could have a mistake in your calculation. Carry out all intermediate results to at least four-digit accuracy to minimize roundoff error, m/s Need Help?Explanation / Answer
From energy: (Uk=Kinetic energy, Us=Spring potential energy)
Uk1 + Uk2 = Us
1/2(m1*v1^2)+1/2(m2*v2^2 )= 1/2k*x^2
so m1*v1^2+m2*v2^2 = k*x^2
plug in known values:
0.25*v1^2 + 0.6*v2^2 = 4.2N/m(0.08m)
From momentum: (p=momentum)
we know that p1=p2
m1*v1 = m2*v2
so v1 = (m2*v2)/m1 or with values v1 = (0.6*v2)/0.25 => v1 = 2.4*v2
when sqaured v1^2 = 5.76*v2^2
plug into the energy equation for v1^2 to find v2. Once found, plug v2 into the momentum to find v1.
0.25*5.76*v2^2 + 0.6*v2^2 = 4.2N/m(0.08m)
v2^2 x 2.04 = 0.336
v2 = 0.4058 m/s
v1 = (0.6*v2)/0.25
v1 = 0.97 m/s
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