Question

A 1 kg body slides from the point A along a horizontal track with an initial speed of 6ms−1 towards a weightless horizontal spring of length 2 m and force constant 4Nm−1.The part AB of the track is frictionless and the part BC has the coefficients of static and dynamic friction 0.22 and 0.2, respectively. Find the total distance through which the block moves before it comes to rest completely (g=10ms−2),

if AB = 4 m and BD = 4.28 m.

if AB = 4 m and BD = 4.28 m.

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Solution

Solution Let total distance travelled be

(4+x)m.

As spring force is conservation

and friction is non-conservative.

△KE+△PE = w friction.

w friction = - Dynamic fraction × distance

in friction through surface

w friction = −(0.2)(1)(10)(×)

w friction = -2x

Initially,

KEi=12mv21=12×1×(6)2=18J

PEi=12k(0)2=0

finally,

KEf=12mvf2=12×1×(0)220J

PEf=12k(0)220

So, (0−18)+(0−0)=−2x

x=9m

Distance travelled = 4+9=13m

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