Problem 34 - Elementary Algebra

Question

Use numerical evaluation on the equations. Physics (momentum) \(p=m v . \) Find \(p\) if \(m=44\) and \(v=9 .\)

Step-by-Step Solution

Answer

Answer: The momentum of the object is 396 kg·m/s.

Step 1: Write down the given values and the formula for momentum

We have the mass \(m = 44 \ \text{kg}\) and the velocity \(v = 9 \ \text{m/s}\). The formula for momentum is \(p = m \cdot v\).

Step 2: Substitute the given values into the formula

Now let's substitute the given mass and velocity values into the formula, like this: \(p = (44 \ \text{kg}) \cdot (9 \ \text{m/s})\).

Step 3: Calculate the momentum

To find the momentum, we need to multiply the given mass and velocity: \(p = (44 \ \text{kg}) \cdot (9 \ \text{m/s}) = 396 \ \text{kg} \cdot \text{m/s}\).

Step 4: Write the final answer

The momentum of the object is \(p = 396 \ \text{kg} \cdot \text{m/s}\).

Key Concepts

Momentum

Momentum is a fundamental concept in physics, describing the motion of an object. It is the product of an object's mass and velocity. Hence, it is often thought of as the "amount of motion" an object has. Momentum, represented by the symbol \(p\), is a vector quantity. This means it has both magnitude and direction.

• The formula to find momentum is \(p = m \cdot v\), where \(m\) is mass (in kilograms) and \(v\) is velocity (in meters per second).
• The direction of momentum is always in the direction of the velocity.
• Without a net external force, the momentum of a system remains constant, demonstrating the conservation of momentum principle.

Understanding momentum helps in analyzing collisions and interactions between objects. It allows physicists to predict how objects will move and interact without necessarily knowing the forces involved.

Numerical Evaluation

Numerical evaluation in physics problems involves calculating specific numerical values by substituting known quantities into formulas. It's an essential skill for solving practical problems. In this exercise, we are asked to find momentum by numerically evaluating the expression \(p = m \cdot v\).

• Start by identifying the given quantities: mass \(m = 44 \ \text{kg}\) and velocity \(v = 9 \ \text{m/s}\).
• Simply substitute these values into the momentum equation: \(p = 44 \cdot 9\).
• The multiplication gives us the momentum: \(p = 396 \ \text{kg} \cdot \text{m/s}\).

Numerical evaluation simplifies complex equations, making them easily applicable to real-world scenarios. It provides us with concrete results which can be further analyzed or used in subsequent calculations.

Equations

Equations are mathematical statements that express the relationship between different quantities. In physics, equations are crucial as they link physical concepts to mathematical formulations. In this particular problem, the focus is on the equation \(p = m \cdot v\) for momentum, which relates mass and velocity to describe motion.

• Equations help in predicting physical phenomena and understanding the mechanics of moving objects.
• They must satisfy the principles of dimensional analysis, meaning the units on both sides of the equation must match.
• By rearranging and solving equations, physicists can discover values of unknown quantities in experiments and practical applications.

Equations are the backbone of physics, providing a structured way to communicate complex ideas and predict outcomes in a quantifiable manner.