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How do you find the unknown mass?

Published in Mass Calculation 3 mins read

To find the unknown mass of an object, you need to use its weight and the acceleration due to gravity.

Calculating Mass from Weight

The relationship between weight, mass, and gravity is fundamental in physics. Here’s how you can determine an unknown mass:

  1. Understand the Formula:

    • Weight (W) is the force exerted on an object due to gravity.
    • Mass (m) is the amount of matter in an object.
    • Acceleration due to gravity (g) is the rate at which objects accelerate towards the ground, approximately 9.8 m/s² on Earth.
    • The formula is: W = m g*

  2. Convert Weight to Newtons:

    • Weight is often measured in units like pounds (lbs) or kilograms (kg), but for calculations in physics, you need to convert the weight to Newtons (N).
      • For example, if the weight is given in kg, then multiply the kg value by the acceleration of gravity, 9.807, to convert to Newtons (N).

  3. Rearrange the Formula to Solve for Mass:

    • The original formula is: W = m g. To solve for mass (m), you rearrange it to: m = W / g*

  4. Divide the Weight (in Newtons) by Gravity (9.8 m/s²):

    • For an object on Earth, divide the weight in Newtons by the acceleration of gravity on Earth (9.8 meters/second²) to find the mass.

Example Calculation

Let's say an object weighs 49 Newtons on Earth. To find its mass:

  1. Weight (W) = 49 N
  2. Acceleration due to gravity (g) = 9.8 m/s²
  3. Mass (m) = W / g
  4. Mass (m) = 49 N / 9.8 m/s² = 5 kg

Therefore, the mass of the object is 5 kilograms.

Practical Insights

  • Weight is a force, while mass is a measure of inertia. The weight of an object will change depending on the gravity, while its mass does not.
  • When you use a scale to measure your weight, it is measuring the force exerted on it due to gravity, but the scale commonly expresses weight in units of mass such as pounds or kilograms.
Step Description Example
1. Convert to Newtons If the weight is given in kg, multiply by 9.807 for Newtons Example: 1 kg * 9.807 = 9.807 N
2. Divide Weight by Gravity Divide the weight in Newtons by the acceleration due to gravity (9.8 m/s²) Example: 9.807 N / 9.8 m/s² = 1 kg

By understanding these steps, you can confidently calculate the unknown mass of an object using its weight and the local gravitational acceleration.

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