Answered

Welcome to Westonci.ca, where curiosity meets expertise. Ask any question and receive fast, accurate answers from our knowledgeable community. Connect with a community of experts ready to help you find solutions to your questions quickly and accurately. Join our Q&A platform to connect with experts dedicated to providing accurate answers to your questions in various fields.

A completely inelastic collision occurs between two balls of wet putty that move directly toward each other along a vertical axis. Just before the collision, one ball, of mass 3.0 kg, is moving upward at 22 m/s and the other ball, of mass 1.3 kg, is moving downward at 11 m/s. How high do the combined two balls of putty rise above the collision point

Sagot :

Answer:

The height balls rise above the collision point, is approximately 7.37 meters

Explanation:

The given parameters just before the collision are;

The mass, m₁ and velocity, v₁ of the ball moving upward are;

m₁ = 3.0 kg, v₁ = 22 m/s

The mass, m₂ and velocity, v₂ of the ball moving downward are;

m₂ = 1.3 kg, v₂ = -11 m/s (downward motion)

The type of collision = Inelastic collision

We note that the momentum is conserved for inelastic collision

Let, [tex]v_f[/tex], represent the final velocity of the balls after collision, we have;

∴ Total initial momentum = Total final momentum

m₁·v₁ + m₂·v₂ = (m₁ + m₂)·[tex]v_f[/tex]

Therefore, we get;

m₁·v₁ + m₂·v₂ = 3.0 kg × 22 m/s + 1.3 kg × (-11) m/s = 51.7 kg·m/s

(m₁ + m₂)·[tex]v_f[/tex] = (3.0 kg + 1.3 kg) ×

∴ 51.7 kg·m/s = 4.3 kg × [tex]v_f[/tex]

[tex]v_f[/tex] = (51.7 kg·m/s)/4.3 kg ≈ 12.023 m/s

The final velocity, [tex]v_f[/tex] ≈ 12.023 m/s

The maximum height, h, the combined balls will rise from the point of collision, moving upward at a velocity of [tex]v_f[/tex] ≈ 12.023 m/s, is given from the kinetic equation of motion, v² = u² - 2·g·h, as found follows

At maximum height, we have;

[tex]h_{max} = \dfrac{v_f^2}{2 \cdot g }[/tex]

Therefore;

[tex]h_{max} \approx \dfrac{12.023^2}{2 \times 9.81 } \approx 7.37[/tex]

The height the combined two balls of putty rise above the collision point, [tex]h_{max}[/tex] ≈ 7.37 m.

We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. We appreciate your time. Please come back anytime for the latest information and answers to your questions. Westonci.ca is your go-to source for reliable answers. Return soon for more expert insights.