A 6 kg mass slides to the right on a surface having a coefficient of friction 0.
ID: 1266109 • Letter: A
Question
A 6 kg mass slides to the right on a surface having a coefficient of friction 0.85 as shown. The mass has a speed of 7 m/s when contact is made with a spring that has a spring constant 177 N/m. The mass comes to rest after the spring has been compressed a distance d. The mass is then forced toward the left by the spring and continues to move in that direction beyond the unstretched position. Finally the mass comes to rest a distance D to the left of the unstretched spring.Find the compressed distance d. The acceleration of gravity is 9.8 m/s2 .
Answer in units of m
A 6 kg mass slides to the right on a surface having a coefficient of friction 0.85 as shown. The mass has a speed of 7 m/s when contact is made with a spring that has a spring constant 177 N/m. The mass comes to rest after the spring has been compressed a distance d. The mass is then forced toward the left by the spring and continues to move in that direction beyond the unstretched position. Finally the mass comes to rest a distance D to the left of the unstretched spring.Find the compressed distance d. The acceleration of gravity is 9.8 m/s2 . Answer in units of mExplanation / Answer
KE of mass= 1/2 *m*v^2. = total initial energy= 147 Joules
PE stored in the spring after compression= 1/2 * k*d^2 = total final energy = 88.5 d^2 Joules
by conservation of energy==> initial energy- final energy= loss due to friction = mu*m*g*d= 49.98 d Joules
==> 88.5 d ^2 +49.98 d-147 = 0
==> d= [-49.98+ sqrt(49.98 ^2- 4 * (88.5)*(-147))]/(2*88.5) = 1.037 m
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