Answer:
vf₁ = - 40 cm/s ; velocity of the 10.9 g object after the collision
vf₁ = 40 cm/s , to the left
Explanation:
Theory of collisions
Linear momentum is a vector magnitude (same direction of the velocity) and its magnitude is calculated like this:
p=m*v
where :
p : Linear momentum
m: mass
v:velocity
There are 3 cases of collisions : elastic, inelastic and plastic.
For the three cases the total linear momentum quantity is conserved:
P₀ = Pf Formula (1)
P₀ :Initial linear momentum quantity
Pf : Final linear momentum quantity
Data
m₁ = 10.9 g : mass of the object₁
m₂ = 17.1 g : mass of the object₂
v₀₁ = 18.5 cm/s , to the right : initial velocity of the object₁
v₀₂= 29.4 cm/s, to the left :initial velocity of the object₂
Problem development
We appy the formula (1):
P₀ = Pf
m₁*v₀₁ + m₂*v₀₂ = m₁*vf₁ + m₂*vf₂
We assume that at the end of the collision the two objects move to the right, so, the sign of the final speeds is positive:
( 10.9 )*(18.5) - ( 17.1)*(29.4) = ( 10.9 )*vf₁ + ( 17.1)*vf₂
-301.09 = (10.9)*vf₁ +(17.1)*vf₂ Equation (1)
Because the shock is elastic, the coefficient of elastic restitution (e) is equal to 1.
[tex]e= \frac{v_{f2}-v_{f1} }{v_{o1}-v_{o2}}[/tex]
1*(v₀₁ - v₀₂ ) = (vf₂ -vf₁)
(18.5 -( -29.4) ) = (vf₂ -vf₁)
47.9 = vf₂ -vf₁
vf₂ = 47.9 +vf₁ Equation (2)
We replace Equation (2) in the Equation (1)
-301.09 = (10.9)*vf₁ +(17.1)*vf₂
-301.09 = (10.9)*vf₁ +(17.1)*(47.9 +vf₁)
-301.09 = (10.9)*vf₁ + 819.09 +17.1vf₁
-301.09-819.09 = (10.9)vf₁ + (17.1 )vf₁
-1120.18 = 28vf₁
vf₁ = -1120.18 / 28
vf₁ = - 40 cm/s ; velocity of the 10.9 g object after the collision
vf₁ = 40 cm/s , to the left
