Question

A block of 4 kg moves in the +x direction with a velocity of 15 m/s while a block of 6 kg moves in the +y direction with a velocity of 10 m/s. They collide and stick together.

Calculate the following: a. What is the momentum in this system? b. What is the final velocity of the two blocks?

Answer 1

a.)

Initial momentum of system is given by,

Pi = m1*v1 + m2*v2

here, m1 = mass of block A = 4 kg

and m2 = mass of block B = 6 kg

v1 = initial velocity of blockA = 15 m/sec. towards +x = (15 i + 0 j) m/sec

v2 = initial velocity of blockB = 10 m/sec towards +y = (0 i + 10 j) m/sec

So, Pi = 4*(15 i + 0 j) + 6*(0 i + 10 j)

Pi = 60 i + 60 j = Momentum of system.

b.)

Since there is no external force applied, So using momentum conservation:

Pi = Pf

Since they stick together after collision, So their final velocity will be same.

then, Pf = 60 i + 60 j

(m1 + m2)*V = 60 i + 60 j

here, V = final velocity of two blocks = ??

V = (60 i + 60 j)/(4 + 6)

V = 6 i + 6 j

magnitude of final velocity = |V| = sqrt(6^2 + 6^2) = 8.5 m/sec.

direction of final velocity = arctan(6/6) = 45 deg from +x direction in counter-clock wise direction.

So, final velocity = 8.5 m/sec. at 45 deg from +x direction in counter-clock wise direction.

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