## Mass vs Weight

Consider you are checking in luggage prior to boarding a flight at sea level. After placing your gear on the scale, the airline agent says your bag “weighs 45 kg”.
1. What is the bag’s mass in SI units?
2. What is the bag’s weight in SI units?
3. How much would the bag weigh on the moon’s surface if the acceleration is 1.62 m/s^2?
4. Explain the differences between mass and weight.

Hint
Mass is how much matter exists inside an object. Weight is the force of gravity on an object.
Hint 2
Newton’s 2nd Law:
$$F=m\cdot a$$$where $$F$$ is the force, $$m$$ is the mass, and $$a$$ is the acceleration. Mass is how much matter exists inside an object, and is typically measured in kg. Weight is the force of gravity on an object, and is typically measured in Newtons. On Earth, we colloquially use them interchangeably, but the two terms have distinctions for technical applications. When the airline agent said the bag “weighs” 45 kg, they were actually providing the mass. To determine weight, we need to solve for force. Newton’s 2nd Law: $$F=m\cdot a$$$
where $$F$$ is the force, $$m$$ is the mass, and $$a$$ is the acceleration.
$$F=(45kg)(9.8\frac{m}{s^2})=441\frac{kg\cdot m}{s^2}=441\:N$$$At sea level, the acceleration due to gravity at a constant $$9.8\:m/s^2$$ . However, the moon’s surface has a lower gravitational field due to its smaller size compared to Earth. Mass is constant throughout the universe, but an object’s weight will depend on the gravitational environment. To find the bag’s weight on the moon, use Newton’s 2nd Law again: $$F=(45kg)(1.62\frac{m}{s^2})=72.9\frac{kg\cdot m}{s^2}=72.9\:N$$$
1. 45 kg
2. 441 N
3. 72.9 N
4. Mass is how much matter exists inside an object and is constant throughout the universe. Weight is the force of gravity on an object and will change based on the gravitational environment.