The value of n = 79
Further explanation
Momentum is the product of the mass of an object and its velocity
p = mv
If 2 objects with mass A and mass B collide with velocity va and vb, then the law of conservation of momentum will occur:
mava + mbvb = mava '+ mbvb' (equation 1
)
can be stated:
the total momentum before the collision is equal to the total momentum after the collision (in the absence of external forces)
Collisions between these 2 objects can be
elastic, inelastic, and completely inelastic (the colliding objects stick together)
For elastic collision applies
va'-vb '= vb - va (equation 2)
Two particles approach each other with equal and opposite speed v. , because the velocity is a vector, then the velocity of objects a and objects b is the same but has a different sign (according to the direction, we consider the right direction positive)
va = v ( to the right)
vb = -v (to the left)
after an elastic collision occurs
va '= -2.95 v ( to the left)
vb '= v' (to the right)
so equation 2 becomes
va'-vb '= vb - va
-2.95v - vb '= -v - v
-2.95v -vb '= -2v
-vb '= - 2v + 2.95v
-vb '= 0.95v
vb '= -0.95v
We input in equation 1 (ma = m, mb = nm)
mava + mbvb = mava '+ mbvb'
m.v-nmv = m.-2.95v + nm. -0.95v -> we divide both segments by m
v-nv = -2.95v-n.0.95v (combine like terms)
v + 2.95v = nv-0.95v
3.95v = n0.05v
n = 3.95v: 0.05v
n = 79
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