Enrol and complete the course for a free statement of participation or digital badge if available. It is possible to calculate the work done on a falling object by the gravitational force. We will adopt a simplifying approach and start by making the assumption that air resistance is negligible.
In fact, air resistance is negligible for many practical purposes, so our calculations here won't be too unrealistic. If an object falls a certain distance, work will be done on it by the gravitational force that is acting on it.
This work will cause the kinetic energy of the object to increase as it falls. It is easy enough to calculate the energy involved. If we take as an example a book falling from a table onto the floor, as illustrated in Figure 4 , we simply need to know the force which is the weight of this book and the distance travelled in the direction of the force which is the height of the table. Suppose that this book has a mass m , and the table top is a distance h above the floor.
Write down an equation for the work W done by gravity on the book as it falls from the table top to the floor. Estimate the work done on this book by gravity if you let it fall from your table to the floor. Box 1, Estimating , contains advice on how to tackle this sort of question. Assuming that air resistance is negligible, what is the kinetic energy of the book just before it hits the floor, and what is its speed at this point?
You were asked to estimate the work done, so you need to estimate values for the mass of this book and for the height of your table. If it does, think again about your estimated values. The kinetic energy just before impact will be equal to the work done, so it is 0. We can work out the speed from this kinetic energy by using the following equation,.
All content. Course content. About this free course 4 hours study. Level 1: Introductory. Course rewards. Free statement of participation on completion of these courses. Create your free OpenLearn profile. Course content Course content. Motion under gravity Start this free course now. Free course Motion under gravity. Figure 5 a Placing a suitcase on a luggage rack involves doing work against gravity.
Activity 5 Calculate the work done in lifting a 12 kg suitcase from floor level up to a luggage rack 2. Previous 2: Work done by gravity.
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But where do you start the h? Where is h equal to 0? The answer is that it doesn't matter. Since it is always only changes we will be calculating with, you can start anywhere. If we are bouncing an object on the floor, it might be convenient to choose the floor as 0. But if we have a table, we might want to choose the table top as 0. If we then drop an object, the h goes negative!
The h is a coordinate of a position. It can be positive or negative. It is only the changes in it that matter. Tip: To turn text into a link, highlight the text, then click on a page or file from the list above. To edit this page, request access to the workspace. Gravitational potential energy Page history last edited by Ben Dreyfus 6 years, 7 months ago. The work done by the gravitational force on the object as it moves through the displacement is To interpret this, it makes more sense to associate the cosine factor with the displacement rather than the force.
So we want to write the work as This makes sense. Gravitational PE Notice that the work done only depends on the initial and final position of the object -- the difference in the heights. This means that we can get away with defining the work as a change in gravitational potential energy -- and this leads us to define a potential energy function for gravity: Making sense -- free fall To make sense of how gravitational PE works, let's consider the special case of free-fall in flat earth gravity; in the case where there are no other forces acting on the object.
This gives the relation: where we have now simplified our notation to have v 0 be the initial velocity and h to be the height it rises. This approach can be very useful in describing any free-fall situation -- even in 2D. Then the total work done along the whole path C can be obtained by summing up i.
Now, in the case of the force being the gravitational force, we know that the work done should only depend on the start and end points of the path remember the path independence property. Now, instead of having a path integral, we simply have an integral only between the start and end points:. In the examples down below, we will indeed see exactly how the idea of path independence works in practice and also how the work done by gravity turns out to always depend on simply the total displacement change in potential energy.
It is known that gravity is what causes an object to fall, which means that the potential energy of the object will change. So, does gravity do work on a falling object then? To put it simply, gravity does do work on every object that is falling due to gravity. The object will start rolling down the plane due to gravity pulling it downwards, so does gravity then do work also on an inclined plane?
In short, gravity does do work on an inclined plane, however, it will only depend on the total change in height. But how exactly is that possible? To find the work done by gravity on the inclined plane as shown above, we use the formula that I gave earlier:. We can actually manipulate the above equation a little bit and see that it simplifies to a quite nice form.
The really interesting thing about the above formula is that the work done by gravity does not actually depend on the incline of the plane at all ; it only depends on the total displacement in the direction of the gravitational force, i. Since the force of gravity is acting on the pendulum, does gravity also do work on a pendulum? In short, gravity does do work on a pendulum for the simple reason that the height of the pendulum bob changes.
Here is essentially what is happening; a pendulum starts swinging from some height h and we wish to calculate what the work done by gravity on this pendulum would be everything we need is in the picture below.
We can also find the displacement of the pendulum bob, which is simply the arc length as given by the picture below. This is a basic trigonometric integral, from which you get after evaluating the limits of integration:.
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