A 1.10 kg mass slides to the right on a surface having a coefficient of kinetic

Question

A 1.10 kg mass slides to the right on a surface having a coefficient of kinetic friction 0.250 (Fig. P8.60). The object has a speed of vi = 3.20 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.
m
(b) Find the speed v at the unstretched position when the object is moving to the left.
m/s
(c) Find the distance D where the object comes to rest.
m

Explanation / Answer

Here,

m =1.1 Kg

uk = 0.250

vi = 3.2 m/s

force constant , k = 50 N/m

a) Using conservation of energy ,

let the distance is d

0.5 * k * d^2 + uk * m * g * d = 0.5 * m * vi^2

0.5 * 50 * d^2 + 0.250 * 1.1 * 9.8 * d = 0.5 * 1.1 * 3.2^2

solving for d

d = 0.423 m

the distance d is 0.423 m

b) let the speed is v

Using conservation of energy

0.5 * 50 * 0.423^2 = 0.5 * 1.1 * v^2 + 0.250 * 1.1 * 9.8 * 0.423

solving for v

v = 2.46 m/s

the speed of the box is 2.46 m/s

c)

let the distance is D

Using conservation of energy

0.5 * 1.1 * 2.46^2 = 0.250 * 1.1 * 9.8 * D

D = 1.24 m

the distance D is 1.24 m

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