Question

What are the weight in newtons and the mass in kilograms of (a) a 5.00-lb bag of sugar, (b) a 240-lb fullback, and \((c)\) a 1.80-ton car? (1 ton \(=2000\) lb. \()\)

Short answer

Weight and Mass are: (a) Bag of Sugar: 22.2 N and 2.27 kg, (b) Fullback: 1068 N and 109 kg, (c) Car: 15972 N and 1630 kg

Step-by-step solution

Convert Pounds to Newtons for Each Item

Use the conversion factor of 4.45 newtons equals 1 pound to convert from pounds to newtons. (a) For the 5.00-lb bag of sugar, the weight will be \(5.00 \times 4.45\) N. (b) For the 240-lb fullback, the weight will be \(240 \times 4.45\) N. (c) For the 1.80-ton car, convert tons to pounds, then to newtons. As 1 ton is 2000 lb, the car weighs \( 1.80 \times 2000 \times 4.45\) N.

Convert Newtons to Kilograms for Each Item

Substitute the weight in newtons in the following formula to find the mass: \( \text{mass(kg)} = \text{weight(N)} / 9.8 \). (a) For the bag of sugar, the mass will now be \(5.00 \times 4.45 / 9.8\) kg. (b) For the fullback, the mass will be \(240 \times 4.45 / 9.8\) kg. (c) For the car, the mass will be \( 1.80 \times 2000 \times 4.45 / 9.8\) kg.

Key concepts

Newton (N) to Kilograms (kg) conversion

Newton is a unit of force, while kilograms refer to mass. When you have the weight of an object in Newtons, you can convert it to mass in kilograms using Earth's gravity as a conversion factor. On Earth, the standard gravitational acceleration is approximately 9.8 m/s².
To convert a weight in Newtons (N) to mass in kilograms (kg), you use the formula:

• \[ \text{mass (kg)} = \frac{\text{weight (N)}}{9.8} \]

Suppose you have an object's weight in Newtons. For example, if something weighs 44.5 N on Earth, its mass would be:

• \[ \text{mass (kg)} = \frac{44.5}{9.8} \approx 4.54 \text{ kg}\]

This conversion is essential for accurately distinguishing between weight (a force) and mass (a property of matter).

Pounds to Newtons conversion

Pounds (lb) are a unit of force commonly used in the United States. When it comes to scientific purposes or international standards, converting to Newtons is necessary. The conversion factor to switch from pounds (lb) to Newtons (N) is approximately 4.45. This means for every pound, you multiply by 4.45 to get the equivalent weight in Newtons.
For example, to convert 5 pounds to Newtons:

• \[5 \times 4.45 = 22.25 \text{ N} \]

This conversion allows you to communicate weight more universally, given that Newtons are part of the metric system which is widely recognized in scientific communities.

Mass and Weight calculation

Mass and weight are related but distinctly different concepts. Mass measures the amount of matter in an object, and it doesn’t change regardless of the object’s location. Weight, on the other hand, is the force exerted by gravity on an object.
The relationship between weight (in Newtons) and mass (in kilograms) on Earth is given by:

• Weight(N) = Mass(kg) × Gravity (9.8 m/s²)

Understanding this relationship is crucial, especially when performing calculations and conversions between different units. If you know the weight of an object and Earth’s gravity, you can rearrange this formula to find the mass in kilograms:

• \[ \text{Mass (kg)} = \frac{\text{Weight (N)}}{9.8} \]

This is helpful in many scientific contexts where knowing the exact mass of an object is necessary for further calculations or experiments.

Metric conversion factors

The metric system is a universal measurement system used widely in science and most countries around the world. Conversion within this system can often involve factors of 10, making it simpler than other systems.
Common metric conversions involve factors like:

• 1 kilometer = 1000 meters
• 1 meter = 100 centimeters
• 1 kilogram = 1000 grams

However, when dealing with force and weight, such as converting pounds to Newtons, it's important to use specific conversion factors like 4.45 to switch from imperial units to metric units effectively.
Utilizing these factors correctly ensures accurate measurements and calculations, making communication of scientific data efficient and less prone to errors.