# 4.25: Mass vs Weight

**At Grade**Created by: CK-12

This is Sam at Newton’s Skate Park. He’s standing on the back end of his skateboard to keep it from tipping over the edge of a half-pipe. The force of his weight pressing down on the skateboard prevents gravity from pulling it over the edge and down the side of the half-pipe.

### Weight, Mass, and Acceleration

**Weight** is a measure of the force of gravity pulling down on an object. It depends on the object’s mass, which is how much matter the object contains. It also depends on the downward acceleration of the object due to gravity, which is the same all over Earth. Weight can be represented by the equation:

F = m × a

This is the general equation that relates force to mass and acceleration. When it relates weight to mass and acceleration, the letter F represents the object’s weight in Newtons (N), which is the SI unit for weight. The letter m in the equation represents the object’s mass in kilograms, and the letter a represents the downward acceleration due to gravity. As this equation shows, weight is directly related to mass. As an object’s mass increases, so does its weight. For example, if mass doubles, weight doubles as well. You can learn more about weight, mass, and acceleration at this URL:

http://www.nasa.gov/mov/192448main_018_force_equals_mass_time.mov

### Calculating Weight

All objects on Earth accelerate downward due to gravity at a rate of 9.8 m/s^{2}. Therefore, if you know the mass of an object, you can calculate its weight using this equation:

F = m × 9.8 m/s^{2}

**Q**: Sam has a mass of 50 kilograms. What is his weight in Newtons?

**A**: You can calculate Sam’s weight in Newtons by substituting his mass in kilograms into the weight formula:

F = m × 9.8 m/s^{2} = 50 kg × 9.8 m/s^{2} = 490 kg *bull; m/s^{2}, or 490 N

You’re probably more familiar with weight in pounds (lb) than in Newtons. One Newton equals 0.225 pounds. In other words, there are 0.225 pounds per Newton. You can use this ratio to convert Newtons to pounds.

**Q**: What is Sam’s weight in pounds?

**A**: In pounds, Sam’s weight is 490 N x 0.225 lb/N = 110 lb.

### Summary

- Weight is a measure of the force of gravity pulling down on an object. It depends on the object’s mass and the acceleration due to gravity, which is 9.8 m/s
^{2}on Earth. - The formula for calculating weight is F = m × 9.8 m/s
^{2}, where F is the object’s weight in Newtons (N) and m is the object’s mass in kilograms. The Newton is the SI unit for weight, and 1 Newton equals 0.225 pounds.

### Explore More

At the following URL, solve the first four problems, and then check your answers. If any of your answers are incorrect, listen to the audio guided solutions.

http://www.physicsclassroom.com/calcpad/newtlaws/problems.cfm

### Review

- What is weight? What is the SI unit for weight?
- Explain how to calculate an object’s weight on Earth from its mass.
- Sam’s older sister Nina, who is pictured in the
**Figure**below, has a mass of 52 kilograms. How much does Nina weigh in Newtons? How much does she weigh in pounds? - The moon has less gravity than Earth. If you were on the moon, how would your weight be different than it is on Earth?

### Image Attributions

- Define weight.
- Show how to calculate the weight of an object from its mass.

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