Theory question 117
Dynamics(a) A ball P moving with velocity 2u ms−1, collides with a similar ball Q, of different mass, which is at rest. After collision, Q moves with velocity u ms−1 and P with velocity ½u ms−1, in the opposite direction. Find the ratio of the masses of P and Q.
(b) Two forces of magnitudes 3N and 7N have a resultant of magnitude 5N. Calculate, correct to one decimal place, the angle between the two forces.
(c) AB = (−4; 6) and CB = (2; −3) are two vectors in the XY plane. If V is the mid-point of AB, find CV.
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(a) Momentum: mP(2u) + 0 = mP(−½u) + mQ(u)
2.5mP = mQ, so mP : mQ = 2 : 5
(b) 5² = 3² + 7² + 2(3)(7)cos θ, so 42 cos θ = −33, cos θ = −0.7857
θ ≈ 141.8°
(c) VB = ½AB = (−2; 3)
CV = CB + BV = CB − VB = (2; −3) − (−2; 3) = (4; −6)
Conserve momentum with P's final velocity negative; for (b) use the resultant formula R² = P² + Q² + 2PQ cos θ.