Academic Integrity: tutoring, explanations, and feedback — we don’t complete graded work or submit on a student’s behalf.

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 m

Explanation / 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

Hire Me For All Your Tutoring Needs
Integrity-first tutoring: clear explanations, guidance, and feedback.
Drop an Email at
drjack9650@gmail.com
Chat Now And Get Quote