A1.50-kg object slides to the right on a surface having a coefficient of kinetic

Question

A1.50-kg object slides to the right on a surface having a coefficient of kinetic friction 0.250 (Figure a). The object has a speed of V_i = 3.10 m/s when it makes contact with a light spring (Figure b) 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. Finally, the object comes to rest a distance D to the left of the unstretched spring (Figure e). Find the distance of compression d. Find the speed v at the unstretched position when the object is moving to the left (Figure d) m/s Find the distance D where the object comes to rest.

Explanation / Answer

mass m = 1.5 kg

co-efficnt of friction n = 0.25

frictional force = n*mg = 0.25*1.5*9.8 = 3.675 N

When the object at the spring vel. v = 3.1 m/s

KE = 0.5 mv2 = 0.5 *1.5*3.12 = 7.21 J

whne the object is pushing the spring to the right , its energy is used to work agianst the frictional force and to compress the spring

When the spring is compressed by d , pot. energy of the spring U = 0.5kd2 = 0.5*50*d2

work done aginst friction W = Fs*d = 3.675d

conserving the total mechanical energy K = W +U

7.21 = 3.675d + 25d2

solving for d = 0.469 m

when the object left contact with the spring its

KE = 5.44 - 3.675*0.469 = 3.716 J = 0.5mv2

speed of the object = 4.955 m/s

when the object moves to the left, the potential energy stored in the spring is used to work agiant the frictional froce

U = Fs*D = 0.5*50 *0.4692 = 5.44 J

D =5.44/3.675 = 1.49 m

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