Question

the ____universe____ the object is.

1. what is mass?

1. what is weight? is weight different from the force of gravity on an object?

1. in tomorrow’s lab, you will hang a known mass off a force sensor as shown on the right. to the right is a free body diagram for the mass as it hangs on the force sensor. based on this free - body diagram, what force does the force sensor measure?

(there are images: one is a diagram of a force sensor with a mass hanging, and the other is a free - body diagram with $f_{sensor}$ (upward) and $f_g$ (weight, downward))

Explanation:

Question 1: What is mass?

Mass is a fundamental physical quantity that measures the amount of matter in an object. It is an intrinsic property, meaning it does not depend on the object's location (e.g., on Earth or in space) and is typically measured in kilograms (kg), grams (g), etc. It relates to an object's inertia, or its resistance to changes in motion.

Weight is the force exerted on an object due to gravity. Mathematically, it is calculated as \( W = mg \), where \( m \) is mass and \( g \) is the acceleration due to gravity (e.g., \( 9.8 \, \text{m/s}^2 \) on Earth). Weight is equivalent to the force of gravity on an object; it depends on the object's location (since \( g \) varies) and is a force (measured in newtons, N).

Step 1: Analyze the Free - Body Diagram

The free - body diagram shows two forces acting on the mass: an upward force \( F_{\text{sensor}} \) from the force sensor and a downward force \( F_g \) (weight) due to gravity. Since the mass is in equilibrium (hanging at rest), the net force on it is zero. By Newton's second law (\( F_{\text{net}}=ma \), and \( a = 0 \) for a stationary object), the upward force from the sensor must balance the downward gravitational force.

Step 2: Relate the Forces

From the equilibrium condition \( F_{\text{sensor}}-F_g = 0 \) (taking upward as positive), we get \( F_{\text{sensor}}=F_g \). The force sensor measures the force it exerts on the mass, which, by Newton's third law (action - reaction), is equal in magnitude and opposite in direction to the force the mass exerts on the sensor. But in terms of the force on the mass, the sensor's force balances the weight, so the sensor measures the weight of the mass (or the gravitational force on the mass, which is equal to the tension - like force it exerts, balancing the weight).

Answer:

Mass is the amount of matter in an object, an intrinsic property (measured in kg/g) related to inertia, independent of location.

Question 2: What is weight? Is weight different from the force of gravity on an object?