Exam Question:

A 0.5 kg object is moving with a velocity of 2 m/s. It strikes a stationary object of mass 0.3 kg. The two objects stick together after the collision. Calculate the final velocity of the combined object.

Answer:

1. Given:

   • Mass of object 1 (m₁) = 0.5 kg
   • Initial velocity of object 1 (v₁) = 2 m/s
   • Mass of object 2 (m₂) = 0.3 kg
   • Final velocity of the combined object (v) = ?

2. Let's calculate the initial momentum (p₁) of object 1:

   Momentum (p) = mass (m) x velocity (v)

   Initial momentum of object 1 (p₁) = m₁ x v₁

   Substituting the given values, we get:

   p₁ = 0.5 kg x 2 m/s = 1 kg·m/s

3. As the two objects stick together after the collision, the final momentum (p) of the combined object is equal to the initial momentum (p₁).

   Final momentum (p) = p₁

   Therefore, p = 1 kg·m/s

4. Now, let's calculate the final velocity (v) of the combined object using the formula:

   Final momentum (p) = mass (m) x velocity (v)

   Rearranging the equation, we get:

   v = p / m

   Substituting the given values, we get:

   v = 1 kg·m/s / (0.5 kg + 0.3 kg) = 1 kg·m/s / 0.8 kg = 1.25 m/s

5. Therefore, the final velocity of the combined object is 1.25 m/s.