Question

A 6.0-kg object moving at 5.0 m/s collides with and sticks to a 2.0-kg object. After the collision the composite object is moving at 2.0 m/s in a direction opposite to the initial direction of motion of the 6.0-kg object. Determine the speed of the 2.0-kg object before the collision. a. 23 m/s b. 15 m/s c. 11 m/s d. 8.0 m/s e. 7.0 m/s

Answer 1

Answer:

a) 23 m/s

Explanation:

• Assuming no external forces acting during the collision, total momentum must be conserved, as follows:

       $p_{o} = p_{f} (1)$

• The initial momentum p₀, can be written as follows:

       $p_{o} = m_{1} * v_{1o} + m_{2}* v_{2o} = 6.0 kg * 5.0 m/s + 2.0 kg * v_{2o} (2)$

• The final momentum pf, can be written as follows:

        $p_{f} = (m_{1} + m_{2} )* v_{f} = 8.0 kg* (-2.0 m/s) (3)$

• Since (2) and (3) are equal each other, we can solve for the only unknown that remains, v₂₀, as follows:

       $v_{2o} = \frac{-6.0kg* 5m/s -8.0 kg*2.0m/s}{2.0kg} = \frac{-46kg*m/s}{2.0kg} = -23.0 m/s (4)$

• This means that the 2.0-kg object was moving at 23 m/s in a direction opposite to the 6.0-kg object, so its initial speed, before the collision, was 23.0 m/s.

Answer 2

The speed of the 2.0-kg object before the collision will be 23 m/s.Option A is correct.

What is the law of conservation of momentum?

According to the law of conservation of momentum, the momentum of the body before the collision is always equal to the momentum of the body after the collision.

The given data in the problem is;

m₁ is the mass of objthe ct = 6.0-kg

v₁ is the speed moving = 5

m₂ is the mass of object 2 = 2.0 Kg

V is the final speed = 2.0 m/s

v₂ is the speed of the 2.0-kg object before the collision =?

According to the law of conservation of momentum;

Momentum before collision =Momentum after collision

$\rm m_1v_1 + m_2v_2 = V(m_1 + m_2)\\\\(6 \times 5) + (2 \times v_2) = -2.0 \times (8) \\\\ \rm v_2 = \frac{-46}{2.0} \\\\ \rm v_2 =-23.0\ m/sec$

Hence the speed of the 2.0-kg object before the collision will be 23 m/s.Option A is correct.

To learn more about the law of conservation of momentum refer;

https://brainly.com/question/1113396