The first mistake occurs in the definition and formula for momentum and velocity, and then in subsequent steps.
1. Definition and formula for momentum and velocity:
- Correct definition: Momentum [tex]\( p \)[/tex] is the product of mass [tex]\( m \)[/tex] and velocity [tex]\( v \)[/tex], so [tex]\( p = m \cdot v \)[/tex].
2. Incorrect equation and solving for velocity:
- Correct equation to solve for velocity: [tex]\( v = \frac{p}{m} \)[/tex].
3. Units and Conversion:
- Since the mass is given in grams, it should be converted to kilograms: [tex]\( 135 \, \text{g} = 0.135 \, \text{kg} \)[/tex].
4. Substitute values:
- [tex]\( v = \frac{p}{m} = \frac{53 \, \text{kg} \cdot \text{m/s}}{0.135 \, \text{kg}} \)[/tex].
5. Calculate:
- [tex]\( v = 392.5926 \, \text{m/s} \)[/tex].
6. Rounding to four significant digits:
- [tex]\( v \approx 392.6 \, \text{m/s} \)[/tex].
So the corrected solution should be:
Problem:
Momentum is mass times velocity. Suppose the momentum of a [tex]\( 135 \, \text{g} \)[/tex] object is measured to be [tex]\( 53 \, \frac{\text{kg} \cdot \text{m}}{\text{s}} \)[/tex]. Calculate the object's velocity.
Be sure your answer has a unit symbol and the correct number of significant digits.
Solution:
Write down the definition of momentum:
[tex]\[ p = m \cdot v \][/tex]
Solve for velocity:
[tex]\[ v = \frac{p}{m} \][/tex]
Convert mass to kg:
[tex]\[ 135 \, \text{g} = 0.135 \, \text{kg} \][/tex]
Substitute the given values:
[tex]\[ v = \frac{53 \, \text{kg} \cdot \text{m/s}}{0.135 \, \text{kg}} \][/tex]
Calculate:
[tex]\[ v = 392.5926 \, \text{m/s} \][/tex]
Round to four significant digits:
[tex]\[ v \approx 392.6 \, \text{m/s} \][/tex]
