A marble is rolling at a velocity of 1.5 m/s with a momentum of 0.10 kg⋅m/s. What is its mass?
Understand the Problem
The question asks us to calculate the mass of a marble given its velocity and momentum. We can use the formula: momentum (p) = mass (m) * velocity (v) to solve for mass (m).
Answer
$0.02 \, \text{kg}$
Answer for screen readers
The mass of the marble is $0.02 , \text{kg}$.
Steps to Solve
- Write down the formula relating momentum, mass, and velocity
The formula is: $$ p = m \cdot v $$ where $p$ is momentum, $m$ is mass, and $v$ is velocity.
- Rearrange the formula to solve for mass
To find the mass $m$, we rearrange the formula: $$ m = \frac{p}{v} $$
- Plug in the given values
We are given $p = 0.1 , \text{kg} \cdot \text{m/s}$ and $v = 5 , \text{m/s}$. Substituting these values into the formula for mass: $$ m = \frac{0.1}{5} $$
- Calculate the mass
$$ m = 0.02 , \text{kg} $$
The mass of the marble is $0.02 , \text{kg}$.
More Information
The mass of the marble is quite small, as expected for a marble. We can convert to grams by multiplying by 1000, so the mass is 20 grams.
Tips
A common mistake is to forget to rearrange the formula correctly. Make sure you isolate the variable you are trying to find (in this case, mass) before plugging in the values. Another mistake could be using the wrong units, but in this case, the units were consistent, so we didn't need to convert anything.
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