A block is pushed along the floor with a velocity Vo slides adistance d after th

Question

A block is pushed along the floor with a velocity Vo slides adistance d after the pushing force is removed. 1) If the mass of the block is doubled but the initialvelocity is not changed what is the distance the block slidesbefore stopping? 2) If the initial velocity of the block is doubled 2Vobut the mass is not changed what is the distance the block slidesbefore stopping? For each case, please explain why this is happening. I'm just having trouble with this, can anyone help?
1) If the mass of the block is doubled but the initialvelocity is not changed what is the distance the block slidesbefore stopping? 2) If the initial velocity of the block is doubled 2Vobut the mass is not changed what is the distance the block slidesbefore stopping? For each case, please explain why this is happening. I'm just having trouble with this, can anyone help?

Explanation / Answer

1) the friction force F = -mg = ma =>a = -g final speed vf = 0, vf2 -v02 =0-v02 =2ad = -2gd => d = v02 / (2g) so d is independ of mass, so,   If the mass of the block is doubled but theinitial velocity is not changed the distance the block slides before stopping is the samed. 2) now v0 ->2v0 =>d1 = (2v0)2 / (2g) = 4d the distance is four times of d. =>d1 = (2v0)2 / (2g) = 4d the distance is four times of d.

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