Weight and Force Calculations

What is the weight of an object with a mass of 50 kg on Earth, where gravity is 9.8 , \text{m/s}^2?

If a ball has a mass of 3 kg, what is the force acting on it while falling freely on Earth?

What is the mass of an object if its weight is 784 N on Earth?

An astronaut weighs 60 kg on Earth. What would be the astronaut’s weight on Mars, where gravity is 3.7 , \text{m/s}^2?

What is the gravitational acceleration on a planet if a spaceship weighing 720,000 N has a mass of 10,000 kg?

If Big Bertha has a weight of 1000 N on Earth, what is her mass?

If an elevator can safely lift 400 kg and four individuals weigh 900 N, 700 N, 800 N, and 600 N, can the elevator lift them together?

An object weighs 200 N on Earth. What would be its approximate mass on another planet with gravity of 4 , \text{m/s}^2?

Weight and Force Calculations

Weight is a force calculated by multiplying mass by acceleration due to gravity (often represented as 9.8 m/s² on Earth).
Formula: Weight = Mass × Gravity
Units: Weight is measured in Newtons (N), mass in kilograms (kg), and gravity in meters per second squared (m/s²).

Calculating Weight from Mass

Example: A 75 kg object on Earth has a weight of 735 N (75 kg × 9.8 m/s²).

Calculating Mass from Weight

Formula: Mass = Weight ÷ Gravity
Example: An object weighing 500 N has a mass of approximately 51 kg (500 N ÷ 9.8 m/s²).

Weight Variations with Gravity

Weight changes depending on the acceleration due to gravity.
Example: An astronaut with a mass of 75 kg has a weight of 120 N on the moon (75 kg × 1.6 m/s²).

Calculating Gravity from Weight and Mass

Formula: Gravity = Weight ÷ Mass
Example: A spaceship with a mass of 9000 kg and a weight of 390,000 N experiences a gravitational acceleration of 43.3 m/s².

Combined Weight Example (Elevator Problem)

To determine if an elevator can lift multiple people, convert each person's weight to mass by dividing by 9.8 m/s², sum these masses, and then compare the total to the elevator's maximum capacity.
Example: Four people with weights of 850 N, 530 N, 740 N, and 610 N have a combined mass of 278.5 kg. This is comfortably below a 300 kg limit, so the elevator can safely lift them.

This quiz covers the fundamental concepts of weight and force calculations, including how to calculate weight from mass and gravity, as well as the reverse process. Explore examples that illustrate how weight varies with different gravitational forces on Earth and the Moon. Test your understanding of these basic physics principles!