Conservation of Energy A 1.30 kg mass slides to the right on a surface having a

Question

Conservation of Energy

A 1.30 kg mass slides to the right on a surface having a coefficient of kinetic friction 0.250. The object has a speed of vi = 3.00 m/s when it makes contact with a light spring that has a force constant of 50.0 N/m. The object comes to rest after the spring has been compressed a distance d. The object is then forced toward the left by the spring and continues to move in that direction beyond the spring's unstretched position. Finally, the object comes to rest a distance D to the left of the unstretched spring.

(a) Find the distance of compression d.


(b) Find the speed v at the unstretched position when the object is moving to the left.


(c) Find the distance D where the object comes to rest.

Explanation / Answer

a.)conserve energy

0.5mv^2 = 0.5 kd^2 + umg*d

0.5*1.3*3^2 = 0.5*50*d^2 + 0.25*1.3*9.81*d

d = 0.424155 m

d = 42.4155

b.) conserve energy

0.5mv1^2 = 0.5mv^2 - umg*2d

0.5*v1^2 = 0.5*3^2 - 0.25*9.81*2*0.424155

v1= 2.199 m/s

c.) force due to friction = force exetrted by spring

0.25*1.3*9.81 = - kD

D = 0.0637 m

D= 6.37 cm

Related Questions

Navigate

• Browse (All)
• Browse C
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.