The distinction between mass and weight was discovered after Jean Richer transported pendulum clocks from Paris to French Guiana in 1671. He found that they ran slower there quite systematically. The effect was reversed when the clocks returned to Paris. Suppose you weigh 199 pounds in Paris. How much weight would you personally lose in traveling from Paris, where g = 9.8095 m/s2, to Cayenne, where g = 9.7808 m/s2
To calculate the change in weight while traveling from Paris to Cayenne, you need to understand the difference between mass and weight.
Mass refers to the amount of matter an object contains, while weight is the force exerted on an object due to gravity. Mass is a scalar quantity and is measured in kilograms (kg), while weight is a vector quantity and is measured in Newtons (N).
The relationship between weight, mass, and gravitational acceleration can be defined by the formula:
Weight = mass * gravitational acceleration
In Paris, the value of gravitational acceleration (g) is 9.8095 m/s2, and your weight is 199 pounds. To calculate your mass in kilograms, you need to convert pounds to kilograms. Each pound is approximately equal to 0.45359237 kilograms.
So, converting your weight in Paris to kilograms:
Weight in kilograms = 199 pounds * 0.45359237 kg/pound
Now that you have your mass in kilograms, you can calculate your weight in Cayenne. In Cayenne, the value of gravitational acceleration is 9.7808 m/s2.
Weight in Cayenne = mass * gravitational acceleration in Cayenne
Weight in Cayenne = (Weight in kilograms) * 9.7808 m/s2
Now, let's calculate:
Weight in kilograms = 199 pounds * 0.45359237 kg/pound = 90.26517063 kg
Weight in Cayenne = 90.26517063 kg * 9.7808 m/s2 = 882.095264 N
Therefore, in traveling from Paris to Cayenne, your weight would decrease by approximately 882.095264 Newtons.
To calculate the weight loss, we first need to determine the difference in the acceleration due to gravity (g) between Paris and Cayenne.
The weight force can be calculated using the formula:
Weight = mass x gravity
Since the mass remains constant, the weight loss will depend on the change in the value of gravity.
Weight in Paris = 199 pounds
Acceleration due to gravity in Paris (g_paris) = 9.8095 m/s^2
Acceleration due to gravity in Cayenne (g_cayenne) = 9.7808 m/s^2
Weight in Cayenne = Weight in Paris x (g_cayenne / g_paris)
Weight in Cayenne = 199 pounds x (9.7808 m/s^2 / 9.8095 m/s^2)
Weight in Cayenne ≈ 198.413 pounds
Therefore, you would lose approximately 0.587 pounds in weight when traveling from Paris to Cayenne.
You would lose weight in proportion to the decrease in g. Mass stays the same but weight is proportional to g.
Multiply the original weight by (9.8095-9.7808)/9.8095. That will be the weight loss.