LESSON 18 Weight & Mass Recall that according to Newton’s Second Law of Motion, the acceleration of an object is proportional to its mass and the force being applied. The object will accelerate in the direction of the applied force. This is summed up in the equation: F = ma The above equation can be rearranged as: a = F/m The above equation implies that the acceleration of an object is directly proportional to the applied force and inversely proportional to its mass. If more force is applied to an object, the greater its acceleration. If the object has a high mass, then it will experience a smaller acceleration with a given force.

The standard international (SI) units for mass are measured in kilograms (kg), while the SI units for acceleration are m/s2. This means that the units for force are kg·m/s2. This unit of force is called a Newton (N). A Newton (N) is the force required to give a mass of one kilogram an acceleration of one metre per second squared. There are 1000 Newtons in a kiloNewton (kN). PROBLEM: A 475 kg car accelerates at a rate of 3.6 m/s2. What force (in kN) is required for this to occur?

PRACTICE: A force of 4. 25 kN is applied to an object PRACTICE: A force of 4.25 kN is applied to an object. If it accelerates at a rate of 12.8 m/s2, then what is its mass?

GRAVITY is a special type of acceleration caused by Earth’s mass GRAVITY is a special type of acceleration caused by Earth’s mass. The accepted value for the acceleration of falling objects is 9.81 m/s2 [down]. For every second an object falls, it gains 9.81 m/s in downward velocity. In the presence of a gravitational field, a mass has weight. Weight an mass are often referred to as the same thing, but they are quite different. MASS refers to the amount of matter present in an object. It is composed of all of the objects protons, neutrons and electrons. Regardless of where the object is, it will always have the same mass, measured in grams or kilograms. Every mass exerts an attractive force on every other mass, but this is a very small and weak force. Earth is so massive that it is able to exert a noticeable force on nearby objects, called weight. WEIGHT refers to the force exerted on a mass in a gravitational field. A given mass has more weight in a stronger gravitational field. For instance, a 75 kg person has a given weight on Earth. If that person goes to the moon, they will experience 1/6th the weight, as the moon has 1/6th the mass of Earth. The same person, however, will still be 75 kg on the moon, as the amount of matter in their body has not changed.

The units for gravity are the same as acceleration (m/s2), while the units for weight are the same as force (N). The equation for weight and force are identical. F = ma W = mg where W = weight (N) m = mass (kg) g = gravity (-9.81 m/s2) PROBLEM: What is the weight of a 75 kg person on Earth?

PRACTICE: On an unknown planet, a 75 kg person has a weight of 243 N PRACTICE: On an unknown planet, a 75 kg person has a weight of 243 N. What is the acceleration due to gravity on that planet?

H.W. Try the following questions. What is the mass of an object that accelerates at a rate of 3.28 m/s2 if 550 N is applied? What is the force applied to a 500.0 kg mass if it accelerates at a rate of 1.60 m/s2? A 1.2 kN force is applied to a 239 kg object. What will the object’s acceleration be? On Earth, what is the mass of a person with a weight of 300.0 N? On Earth, what is the weight of a 64.5 kg person? On the moon, a 64.5 kg person has a weight of 105 N. What is the gravity of the moon?