* 1. “The Earth has a gravitational field that exerts a force on objects both on and around it.”
Students learn to “define weight as the force on an object due to a gravitational field.”
Mass is the amount of matter in a body whereas weight is the force due to gravity acting on a mass. Mass will not change where the acceleration due to gravity is different but the weight will change.
For example, bathroom weights are calibrated in kg, but actually measure weight as they work by the mass on them compressing the spring. Therefore, it takes into account Earth’s gravitational pull. On the Moon, the gravitational force is about 1/6 that of Earth, so the spring will compress about 1/6 as much. The scales will therefor read 1.6kg instead of 10kg.
W = mg where W = weight, m = mass, g = acceleration due to gravity.
Astronauts in space appear weightless even though gravity is acting on them. At the height of a typical space station gravity is about a third of its value on Earth. The astronauts appear weightless because they are falling around the Earth with the same acceleration as their space station. You could get the same situation on Earth if you were in a lift when the cable broke.
True weight is equal to mg for whatever value g has at that location. Apparent weight is equal to the reaction force exerted on the object and is equal to mg + ma where ‘a’ is the upward acceleration of the object. (For an object accelerating down, a is negative)
Students learn to “explain that a change in gravitational potential energy is related to work done.”
When an object is lifted in a gravitational field the work done is equal to the increase in gravitational potential energy. If an object falls then the gravitational field does work on the object. The amount of work done by the gravitational field is equal to the amount of work required to restore the object to its original position.
Consider the work done in moving an object from the Earth's surface to a height, h metres.
W = F × d
Therefore, W = Fg × d (where Fg is the weight of the object) Fg = mg (as weight of the object = mass x acceleration due to gravity) Therefore, W = mg × d
Therefore, W = mgh (h is the distance the object has been moved)
Students learn to “define gravitational potential energy as the work done to move an object from a very large distance away to a point in a gravitational field. Ep = -G m1m2/r”
Gravitational potential energy is the work required to bring an object from infinity to that point. Since gravity does work on the object the potential energy is negative.
Where Ep = potential energy, G = universal gravitational constant, m1 and m2 are the masses of the two objects and r = distance between the centres of mass of the two objects.
The gravitational potential energy of an object can only be zero, when its distance from a planet is infinite. As the object then falls towards the planet, its gravitational potential energy will decrease (its kinetic energy increases). If GPE decreases from zero, it must become negative in value.
NOTE: If we chose a planet’s surface as the ‘zero level’, Ep has a positive value. If infinity is chosen as the ‘zero level’, then Ep has a negative value.
Students: “Perform an investigation and gather information to determine a value for acceleration due to gravity using pendulum motion or computer-assisted technology and identify reason for possible variations from the value 9.8 ms-2. ” (syllabus)
Suspend a pendulum bob from a fixed support by means of a light thread. Adjust the length of the thread so that the distance from the support to the centre of mass of the bob is 50 cm. Draw the bob a little (less than 5o) to the side and release it. Use a stopwatch to time 10 complete to and fro oscillations of the bob. Repeat the procedure twice more to obtain a total of three readings. Determine the average period by dividing...