IIT JEE , AIEEE Forum - Physics , Mechanics

amitp91

a strip of wood of length L is placed on smooth horizontal surface . an insect starts from one end of the strip , walks with constant veloity and reaches the other end in time T . it then flies off vertically . the strip moves a further distance L in time t
a)T = t
b)t < T
c)t>T
d)depending on the massesd of the insect and the strip
give solution

karthik2007

Please see the next post

amitp91

are u sure ????

karthik2007

Oops, sorry, I mis read the question.

Here is the solution.

If x is the distance moved by the plank:

we have Mx = mL or x = mL/M

now, assuming m>M ie mass of plank is greater than mass of insect, it is easy to see that the plank moves a distance less than L in the time t. Hence, it should be option c)

annihilator

Karthik could explain how you got the equation??

amitp91

so the answer is t >T ?
if yes u are right i have rated u
can u explain what is Mx =mL

karthik2007

yes, answer is t>T

amitp91

please explain what is Mx =mL

karthik2007

As for your question:

1. See, consider the insect and the plank as a system.

2. Now, observe the forces acting on the system. We have the weight of the system acting downward, and the Normal force acting upward, hence they cancel out. So, we have nothing to do with them.

3. The insect is moving on the plank. This is an internal activity, ie, it is taking place within the system. Note that we have taken the insect+plank as our system.

4. Hence, we have only internal forces acting on the system, and thus, the Center of mass of the system will remain at rest, as there is no external force acting on the system (only internal forces act, ie, by the insect)

5. Hence, we are now free to use the fact that the center of mass stays at rest. Now, the insect moves a distance of L towards the right, so let the plank move some distance x towards left.

As COM is at rest: Mx + mL = 0 or x = -mL/M (- sign signifies the left hand side direction)

As m/M <1, it is easy to see that t>T.

Digest the theory that I've tried to explain. The problem is very simple.

karthik2007

get back if you didn't understand it completely.

amitp91

if m/M is < 1 then how t>T

karthik2007

See, in time T, the plank covers a distance of mL/M, which is lesser than L.

Hence, to cover a distance L, it will need more time!

amitp91

thanks karthik

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