A 1.30 kg object sides to the right on a surface having a coefficient of kinetic

Question

A 1.30 kg object sides to the right on a surface having a coefficient of kinetic friction 0.250. The object has a speed of v_1 = 2.90 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 (Figure c). The object is then forced toward the left by the spring (Figure d) and continues to move in that direction beyond the spring's unstretched position, the object comes to rest a distance D to the left of the unstretched spring (Figure e). (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

Kinetic energy of mass = work absorbed by spring + energy to overcome friciton
KE = Ws + Wf
1/2*mV^2 = 1/2kd^2 + mue*mgd

1/2*1.3*2.9^2 = 1/2*50*d^2+0.25*1.3*9.8*d

25d^2+3.185d-5.47 = 0

solution is d = 0.408 m

b) Ws = KE + Wf

1/2*50*0.408^2 = 1/2*1.3*v^2+0.25*1.3*9.8*0.408

v = 2.1 m/s

c) (mue)(mg) = ma

a = mue*g = 2.45 m/s^2

v^2-u^2 = 2aD

D = 2.1^2/2*2.45 = 0.9 m

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