Answer:
3.8226 m/s
Explanation:
Momentum is conserved hence
equating momentum, p
p (before) = p (after)
0 = (m1v1)+(M2v2) but m2=2.77m where m and v are the masses and velocity respectively
0 = (mv1) +(2.77m)(1.38)
(mv1)=-(2.77m)(1.38)
(v1)=-(2.77)(1.38)
Solving v1
v1 = - 3.8226 m/s
= 3.8226 m/s, to the left
According to the law of conservation of linear momentum, the linear
momentum of the blocks is conserved (remains the same).
Reasons:
Mass of the two blocks are; m and M = 2.77·m
Location of the spring = Between the blocks
Speed of the block of mass M after the cord is burned, v₂ = 1.38 m/s
Required:
The speed of the block of mass m
Solution:
According to the law of conservation of linear momentum, we have;
Initial momentum of the blocks = Final momentum after the cord is burned
The initial velocity of the blocks when secured, v₀ = 0
v₁ = The velocity of the block of mass m
Therefore;
(m + M) × 0 = m·v₁ + M × 1.38 = m·v₁ + 2.77·m × 1.38 = m·v₁ + 3.8226·m
(m + M) × 0 = 0
Which gives;
(m + M) × 0 = 0 = m·v₁ + 3.8226·m
m·v₁ + 3.8226·m = 0
m·v₁ = -3.8226·m
v₁·m = -3.8226·m
By comparison of the coefficient of m in the above equation, the velocity of the block of mass m, v₁ = -3.8226 m/s.
Therefore, the magnitude of the velocity of block m, |v₁| = 3.8226 m/s
The direction in which the block of mass m moves = opposite to the direction of the block of mass M.
Given that speed is a scalar quantity, we have;
Learn more about the law of conservation of linear momentum here:
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