What is the mass of a ball moving at 4 m/s with a momentum of 48 kg m/s?
Understand the Problem
The question is asking for the mass of a ball that has a specific momentum and speed. To find the mass, we can use the formula for momentum, which is the product of mass and velocity (momentum = mass × velocity). Here, the momentum is given as 48 kg m/s and the velocity is 4 m/s, so we need to solve for mass.
Answer
The mass of the ball is $12 \, \text{kg}$.
Answer for screen readers
The mass of the ball is $12 , \text{kg}$.
Steps to Solve
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Identify the momentum formula The formula for momentum ($p$) is given by: $$ p = m \cdot v $$ where $m$ is mass and $v$ is velocity.
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Rearrange the momentum formula to solve for mass To find the mass, rearrange the formula: $$ m = \frac{p}{v} $$
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Substitute the given values Substitute the known values into the formula. Here, the momentum $p = 48 , \text{kg m/s}$ and the velocity $v = 4 , \text{m/s}$: $$ m = \frac{48 , \text{kg m/s}}{4 , \text{m/s}} $$
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Perform the calculation Calculate the mass: $$ m = \frac{48}{4} = 12 , \text{kg} $$
The mass of the ball is $12 , \text{kg}$.
More Information
This result indicates that when a ball is moving with a velocity of $4 , \text{m/s}$ and has a momentum of $48 , \text{kg m/s}$, its mass is $12 , \text{kg}$. Momentum is a product of mass and velocity, highlighting how they relate in physics.
Tips
- Mixing up the momentum formula by misplacing mass and velocity.
- Forgetting to perform the division correctly, which could lead to incorrect mass calculation.
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