Mechanical Engineering - Engineering Mechanics - Discussion

IF m<M & v,V are their velocity respectively.

1/2(mv^2)=1/2(MV^2).

m.v*v=M.V*V.
if m<M,in order to get same K.E, v>V.

Now,
p.v=P.V (p=m.v & P=M.V).
as v>V, in order to get same K.E,
So, P>p.

How can you say that v1 = v2.

1/2 m1 v1^2 = 1/2 m2 v2^2.

As m1>m2 So v2 must be >v1.

m1.v1/m2.v2=v2/v1 will have value greater than 1. So m1.v1>m2.v2.

@Suresh.

Given, K.E1 = K.E2, also m1>m2, K.E1 = 1/2m1v1^2, K.E2 = 1/2m2v2^2.

In order to get both the KE equal, their Velocity should be equal since m1>m2 (given). Therefore, Momentum, m1v1 > m2v2.

Simply.

Momentum is related to mass and velocity.

If mass and velocity increase then momentum will increase.

So finally, m1>m2.

Simple greater the mass greater the momentum.

K.E= p^2/2*m.
KE1=KE2.
P1^2/2*m1=P2^/2*m2.
since m1>m2.
So P1>P2.

(1/2)m1v1^2 = (1/2)m2v2^2 (equation showing the equal kinetic energy where m1>m2).

By cancelling (1/2) on both sides, we get,

m1v1^2 = m2v2^2.
p1v1 = p2v2 = constant (denoting p = mv which is momentum).

So, to make the product of two quantities equal, p1>p2.

To avoid complications assume initial values of m1 & m2 as 4 & 1 then we get velocity ratio(v2/v1) as 2 (K.E.=const) consider v1 as & v2 as 2. then m1v1=4 & m2v2 = 2.

The kinetic energy is a function of mass M and velocity V^2, so if we assume the kinetic energy to be the same for both M1 and M2 and fix the velocity such that V1=V2 the M1 = M2, that is True.

So, if we FIX the velocity such that V1=V2, and M1>M2 it is also true that the KE of Object 1> KE of object 2.

So, finally, If the KE of object 1 = KE of object 2, and M1>M2, then the V2>V1 so that object 2 can make up the remainder of the energy that object 1 gets from its mass being greater.

Since V2>V1 the V2/V1 >1.
Thus with KE = 1/2 MV^2 or PV/2.
the KE1=KE2 or P1V1/2=P2V2/2 get rid of the 1/2 since its constants then,

M1V1V1= M2V2V2 divide both sides by V1 so, M1V1 = M2V2*(V2/V1) where V2/V1 has to be greater than 1 as shown above.

So conclusion, P1=P2(V2/V1), where V2/V1 is greater than 1 nd we get P1>P2.