5 Momentum Problems Solved: Physics Worksheet Answers

In the realm of physics education, understanding momentum can be one of the most pivotal and often challenging concepts for students. Momentum, often described as "mass in motion," involves several intricate calculations and conceptual understanding that can baffle even the brightest of students. In this comprehensive blog post, we delve into five common momentum problems, providing detailed solutions to help you grasp this fundamental physics principle.

Problem 1: Calculating Momentum

Momentum (p) is defined as the product of an object’s mass (m) and its velocity (v). Let’s consider an object with a mass of 2 kg moving at a velocity of 3 m/s:

• Given: mass (m) = 2 kg, velocity (v) = 3 m/s
• Formula: p = m × v
• Solution: p = 2 kg × 3 m/s = 6 kg·m/s

The object has a momentum of 6 kg·m/s.

🔍 Note: Momentum is a vector quantity, meaning it has both magnitude and direction.

Problem 2: Impulse and Change in Momentum

Impulse (J) is the change in momentum of an object when a force is applied over a period of time. Consider a hockey puck with an initial momentum of 0 kg·m/s struck with a force of 10 N for 0.2 seconds:

• Given: Initial momentum (p_i) = 0 kg·m/s, Force (F) = 10 N, Time (t) = 0.2 s
• Formula for Impulse: J = F × t
• Solution: J = 10 N × 0.2 s = 2 kg·m/s

The impulse applied to the puck results in a change in momentum of 2 kg·m/s.

🔍 Note: Impulse relates directly to the area under the force-time graph, emphasizing the concept of force applied over time.

Problem 3: Conservation of Momentum

In an isolated system, where no external forces are acting, conservation of momentum states that the total momentum before an event is equal to the total momentum after the event. Let’s look at a two-cart system where cart A (mass 2 kg) moving at 5 m/s collides with cart B (mass 3 kg) at rest:

• Given: m_A = 2 kg, v_A = 5 m/s; m_B = 3 kg, v_B = 0 m/s
• Formula: p_initial = p_final
• Solution:
  • Initial momentum: p_Ai + p_Bi = 2 kg × 5 m/s + 3 kg × 0 m/s = 10 kg·m/s
  • If they stick together after the collision, combined mass = 5 kg
  • Final velocity: v_f = 10 kg·m/s ÷ 5 kg = 2 m/s

🔍 Note: The total momentum is conserved in both elastic and inelastic collisions; however, kinetic energy is only conserved in elastic collisions.

Problem 4: Momentum in Multiple Dimensions

Momentum can also be analyzed in multiple dimensions. If a particle with a mass of 1 kg moves in a vector direction with components v_x = 3 m/s and v_y = 4 m/s:

• Calculate the magnitude of momentum:
  • p_x = m × v_x = 1 kg × 3 m/s = 3 kg·m/s
  • p_y = m × v_y = 1 kg × 4 m/s = 4 kg·m/s
  • Magnitude of momentum: |p| = √(p_x² + p_y²) = √(3² + 4²) = 5 kg·m/s

🔍 Note: This method applies to all dimensions, providing a comprehensive view of an object’s motion.

Problem 5: Momentum in Explosions

An explosion demonstrates how momentum is conserved even when objects move apart. If two cars (each with a mass of 1000 kg) are initially stationary and then move away from each other after an internal explosion, with one car moving at 5 m/s:

• Given: m₁ = 1000 kg, m₂ = 1000 kg, v_1i = v_2i = 0 m/s, v_1f = 5 m/s
• Solution:
  • Initial momentum: p_initial = 1000 kg × 0 m/s + 1000 kg × 0 m/s = 0 kg·m/s
  • Final momentum: p_1f + p_2f = 1000 kg × 5 m/s + 1000 kg × v_2f = 0 kg·m/s
  • v_2f = -5 m/s (because they move in opposite directions, momentum must balance to zero)

🔍 Note: This example shows that internal forces do not change the total momentum of the system.

Key Takeaways from Momentum Problems

In summary, momentum problems in physics allow students to apply theoretical concepts in practical scenarios. Here are the key points:

• Momentum is defined as the product of mass and velocity, which can be extended to various dimensions and conserved in isolated systems.
• The change in momentum is directly related to the impulse applied to an object, which is useful for understanding collisions and explosive events.
• Momentum conservation provides a fundamental principle to solve complex interactions between objects, ensuring that the total momentum remains constant even when the system’s configuration changes.

The exploration of these problems not only enhances your understanding of momentum but also prepares you for more complex physics concepts. By solving such problems, you gain insight into how physical laws govern the universe's dynamics, from the smallest particle interactions to the largest celestial events.

Why is momentum a vector quantity?

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Momentum is a vector quantity because it has both magnitude (mass times velocity) and direction. The direction of momentum is the same as the direction of velocity.

How does impulse differ from force?

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Impulse is the product of force and the time over which it acts. While force is a push or pull on an object, impulse accounts for how long that force is applied, resulting in a change in momentum.

What’s the difference between elastic and inelastic collisions?

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In an elastic collision, both momentum and kinetic energy are conserved. In an inelastic collision, momentum is conserved, but some kinetic energy is transformed into other forms, like heat or sound, and is not conserved.