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Two particles B and C have mass m kg and 3 kg respectively - Edexcel - A-Level Maths Mechanics - Question 1 - 2011 - Paper 1
Question 1
Two particles B and C have mass m kg and 3 kg respectively. They are moving towards each other in opposite directions on a smooth horizontal table. The two particles... show full transcript
Worked Solution & Example Answer:Two particles B and C have mass m kg and 3 kg respectively - Edexcel - A-Level Maths Mechanics - Question 1 - 2011 - Paper 1
Step 1
(a) the value of m
Answer
To find the value of m, we can use the principle of conservation of momentum which states that the total momentum before the collision is equal to the total momentum after the collision.
The momentum before the collision is:
-
For particle B:
P_B = m imes v_B = m imes 4 \ -
For particle C:
P_C = m imes v_C = 3 imes (-2) \
So, total momentum before the collision is:
The momentum after the collision is:
-
For particle B:
P_B' = m imes 1\ -
For particle C:
P_C' = 3 imes 3 \
Total momentum after the collision is:
Setting the total momentum before and after equal gives:
From which:
So,
Step 2
(b) the magnitude of the impulse received by C
Answer
The impulse received by an object can be calculated using the change in momentum.
The initial momentum of particle C before the collision is:
After the collision, the momentum of particle C is:
The change in momentum (which equals the impulse received) for particle C is given by:
Substituting in the values:
Thus, the magnitude of the impulse received by C is:
.