(1) The total momentum of the balls after collision is 3 kg.m/s
(2) The momentum of the object is 100 kg.m/s
(3) The change in the car's momentum is equal to change in the rock's momentum in opposite direction.
(4) The total momentum of the objects is 0 kg.m/s
(5) The mass of the object is 20 kg.
(1) From the principle of conservation of linear momentum, total initial momentum before collision is equal to the momentum after collision.
initial momentum = final momentum
Thus, the total momentum of the balls after collision is 3 kg.m/s
(2) Linear momentum is defined as the product of mass and linear velocity of an object.
momentum of the object is calculated as;
P = mv
P = 5 x 20
P = 100 kg.m/s
(3) Apply the principle of conservation of linear momentum;
[tex]m_1u_1 + m_2u_2 = m_1v_1 + m_2 v_2[/tex]
In order to ensure that momentum is conserved;
- if u₁ is smaller than u₂, then v₁ must be greater than v₂
Let u₁ represents the initial velocity of the small rock and u₂ is the initial velocity of the moving car. In this case, the momentum of the car is bigger.
To conserve the momentum, the final velocity of the rock v₁ must be greater than the final velocity of the car. When this happens, the rock will experience a large change in velocity.
From the equation above will have;
[tex]m_1u_1 + m_2u_2 = m_1v_1 + m_2 v_2\\\\m_1u_1 - m_1v_1 = m_2v_2 - m_2u_2\\\\\Delta P_{rock} = \Delta P_{car}[/tex]
Thus, the change in the car's momentum is equal to change in the rock's momentum in opposite direction.
(4) In a closed system the momentum will be conserved;
Initial momentum = final momentum
Total momentum = final momentum + Initial momentum
The total momentum = 1 x 1.8 + 1 x (-1.8)
Note: the negative sign is because one is moving in opposite direction
The total momentum = 1.8 kg.m/s - 1.8 kg.m/s = 0 kg.m/s
(5) The mass of the object is calculated as;
[tex]m = \frac{P}{v} \\\\m = \frac{100}{5} \\\\m = 20 \ kg[/tex]
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