An object is attached to a trolley with a 0.80 kg mass, which is then pushed into an identical trolley at a speed of 1.1 m / s. The two trolleys couple together and move at a speed of 0.70 m / s after the collision. Calculate the mass of the object. Please help!!
Answers
Given info : An object is attached to a trolley of mass 0.8 kg , which is then pushed into an identical stationary trolley at a speed of 1.1 m/s. The two trolley couple together and move at a speed of 0.70 m/s after the collision.
To find : the mass of the object is...
solution : before collision,
linear momentum of system = linear momentum of object + trolley + linear momentum of trolley
= (m + 0.80 ) kg × 1.1 m/s + 0
= (m + 0.8) × 1.1 Kgm/s
after collision,
linear momentum of system = linear momentum of (object + trolley + trolley)
= (m + 0.8 × 2) kg × 0.7 m/s
= (m + 1.6) × 0.7 kg m/s
∵ external force acting on the system of trolley and object is zero.
linear momentum must be conserved.
so, (m + 0.8) × 1.1 Kgm/s = (m + 1.6) × 0.7 Kgm/s
⇒1.57 m + 1.57 × 0.8 = 0.7m + 0.7 × 1.6
⇒0.87m = 0.136
⇒m = 0.15632 ≈ 0.156 kg
Therefore the mass of object is 0.156 kg
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