How to calculate impulse with mass and velocity?

Understand the Problem

The question is asking how to determine impulse, which is a physics concept calculated using the formula Impulse = Mass x Change in Velocity. We will identify the proper variables and the calculation process involved.

Answer

$40 \, \text{kg} \cdot \text{m/s}$

Steps to Solve

Identify the variables Determine the mass and the change in velocity.

Let's assume the mass, $m$, is given in kilograms (kg).
The change in velocity, $\Delta v$, is calculated as the final velocity ($v_f$) minus the initial velocity ($v_i$) and should be in meters per second (m/s).

Formula for impulse Impulse can be calculated using the formula:

$$ Impulse = m \times \Delta v $$

Substituting for $\Delta v$, we get:

$$ Impulse = m \times (v_f - v_i) $$

Plug in the values Insert the values of mass and velocity into the impulse formula.

For example, if $m = 5 , \text{kg}$, $v_f = 10 , \text{m/s}$, and $v_i = 2 , \text{m/s}$, the equation becomes:

$$ Impulse = 5 , \text{kg} \times (10 , \text{m/s} - 2 , \text{m/s}) $$

Perform the calculation Calculate the change in velocity, then multiply by the mass.

Change in velocity:

$$ \Delta v = 10 , \text{m/s} - 2 , \text{m/s} = 8 , \text{m/s} $$

Now calculate impulse:

$$ Impulse = 5 , \text{kg} \times 8 , \text{m/s} $$

Final result Complete the calculation to find the impulse.

Perform the final multiplication:

$$ Impulse = 40 , \text{kg} \cdot \text{m/s} $$

The impulse is $40 , \text{kg} \cdot \text{m/s}$.

More Information

Impulse is an important concept in physics, as it links the forces acting on an object to its change in momentum. It is a vector quantity, which means it has both magnitude and direction. The unit of impulse is the same as momentum, which is measured in kilograms meter per second ($\text{kg} \cdot \text{m/s}$).

Tips

Confusing mass with weight. Remember, mass is measured in kilograms (kg), while weight is a force measured in newtons (N).
Not properly calculating the change in velocity, which can lead to incorrect impulse values.
Forgetting that impulse is a vector quantity and should consider direction when applicable.

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