0625 · 1.3Mass and weight

Mass, weight and gravitational force

0:00Imagine taking your school bag from Earth to the Moon without adding or removing anything. It contains exactly the same books, but the gravitational pull on it is smaller. Its mass stays the same, while its weight decreases. By the end of this video, you will understand that distinction, calculate weight, and explain how a balance compares masses. We need just two ideas before we begin. A force is a push or a pull, and forces are measured in newtons.

0:25Acceleration means a change in velocity per unit time. These ideas help us explain both the gravitational force on an object and what happens when that object falls freely. First, let us define mass precisely. Mass is a measure of the quantity of matter in an object at rest relative to the observer. For our examples, think of a school bag resting beside you while you measure it. Its mass describes how much matter it contains, and we measure mass in kilograms.

0:52Adding another book increases the school bag's mass because you have added matter. Simply carrying the unchanged school bag somewhere else does not remove any matter. Mass also measures resistance to change in motion, so a larger mass is harder to accelerate under the same force. We will explore that connection further in the video on forces. Weight is a gravitational force on an object that has mass. Near Earth's surface, this force acts downwards, towards the centre of Earth.

1:18Unlike mass, weight describes an interaction between the object and its surroundings. Because weight is a force, its unit is the newton, not the kilogram. This distinction explains why travelling to the Moon changes weight but not mass. The Moon produces a weaker gravitational pull on the same school bag. The school bag still contains the same matter, but the force on that matter is smaller. Mass belongs to the object, while weight depends on the gravitational field where the object is.

Gravitational field strength and weight

1:45Now we are developing the Supplement concept for Extended students. A gravitational field is a region in which a mass experiences a gravitational force. Weight is the effect of a gravitational field on a mass. The object does not need to touch Earth for Earth's field to exert this force on it. To describe the strength of a gravitational field, we consider the force it exerts on each kilogram of mass.

2:08Gravitational field strength is force per unit mass. Near Earth's surface, it is about nine point eight newtons per kilogram. That means each kilogram experiences a gravitational force of about nine point eight newtons. Two kilograms experience twice the force of one kilogram in the same gravitational field. Three kilograms experience three times the force. Each additional kilogram contributes the same amount of weight when the field strength is unchanged.

2:33This is why weight is proportional to mass at a particular location. The defining equation is gravitational field strength equals weight divided by mass. Dividing the total force by the mass tells us the force on each kilogram. Rearranging gives weight equals mass multiplied by gravitational field strength. We can also calculate mass by dividing weight by gravitational field strength. These equations describe a relationship, rather than three separate facts to memorise.

3:01Mass tells us how many kilograms there are, and field strength tells us the force on each kilogram. Multiplying them gives the total gravitational force. Dividing reverses that calculation when either the mass or the field strength is unknown. Let us calculate the weight of a school bag with a mass of two kilograms. The gravitational field strength is nine point eight newtons per kilogram. We choose weight equals mass multiplied by gravitational field strength because we know both quantities.

3:28Substituting gives 2 × 9.8, so the weight is nineteen point six newtons. Notice why the answer is in newtons. We multiplied a mass in kilograms by a force per kilogram. Each of the two kilograms contributes nine point eight newtons to the total force. Always use the field strength given in the question, rather than automatically replacing it with a remembered value. Now consider a rock with a mass of seven point five kilograms on another planet.

3:55Its weight there is forty-five newtons, and we must calculate the gravitational field strength. We use gravitational field strength equals weight divided by mass. Dividing forty-five by seven point five gives six newtons per kilogram. So each kilogram experiences six newtons of gravitational force. Gravitational field strength is also equivalent to the acceleration of free fall. Free fall means that gravity is the only force acting on the object. Near Earth's surface, a field strength of nine point eight newtons per kilogram corresponds to an acceleration of nine point eight metres per second squared.

4:28These describe the same gravitational effect in two different ways. A stronger gravitational field produces a greater free-fall acceleration. In the same field, a larger mass has more weight, but also more resistance to acceleration. Those effects balance, so objects have the same free-fall acceleration when gravity is the only force acting. Air resistance can change their motion, so ordinary falling objects are not always in free fall.

Balances, common mistakes and exam answers

4:54Weights, and therefore masses, may be compared using a balance. Place an object on one pan of an equal-arm balance and standard masses on the other. When the balance is level, the downward forces on the two sides are equal. Both sides experience the same gravitational field strength, so equal weights correspond to equal masses. Move that balance and its contents to the Moon, and both weights decrease by the same proportion.

5:17The balance still compares their masses correctly because the field strength is the same for both pans. A force meter, by contrast, measures force and can display weight in newtons. An instrument that displays kilograms is giving a reading of mass, not weight. Watch for three common mistakes. Saying an object weighs two kilograms confuses a mass unit with a force unit. Saying its mass decreases on the Moon confuses the unchanged amount of matter with the reduced gravitational force.

5:44Saying a stationary object has no weight is also wrong, because gravity can act even when the object is not moving. An exam-style question might ask you to state what mass means and explain why an object weighs less on the Moon. Identify the command words before answering. State calls for the definition, while explain calls for a reason. Link the smaller weight to the weaker gravitational field, rather than just saying that the object feels lighter.

6:09A precise answer would be these four sentences. Mass is a measure of the quantity of matter in an object at rest relative to the observer. Its mass is unchanged because the quantity of matter is unchanged. The gravitational field strength on the Moon is smaller than on Earth. Since weight equals mass multiplied by gravitational field strength, its weight is smaller. Let us bring everything together. Mass measures the quantity of matter and is measured in kilograms.

6:35Weight is the gravitational force on a mass and is measured in newtons. Gravitational field strength tells us the force per unit mass, and multiplying it by mass gives weight. A balance compares weights in the same field, allowing us to compare masses.