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We have seen that work done by or against the gravitational force depends only on the starting and ending points, and not on the path between, allowing us to define the simplifying concept of gravitational potential energy. Finally, note that speed can be found at any height along the way by simply using the appropriate value of h at the point of interest. Third, and perhaps unexpectedly, the final speed in part (b) is greater than in part (a), but by far less than 5.00 m/s. For example, the roller coaster will have the same final speed whether it falls 20.0 m straight down or takes a more complicated path like the one in the figure. When friction is negligible, the speed of a falling body depends only on its initial speed and height, and not on its mass or the path taken. Second, only the speed of the roller coaster is considered there is no information about its direction at any point. This is quite consistent with observations made in Chapter 2.7 Falling Objects that all objects fall at the same rate if friction is negligible. More precisely, we define the change in gravitational potential energy ΔPE g to be (b) As the weight moves downward, this gravitational potential energy is transferred to the cuckoo clock. (a) The work done to lift the weight is stored in the mass-Earth system as gravitational potential energy.

(See Example 2.) This shortcut makes it is easier to solve problems using energy (if possible) rather than explicitly using forces. We will find it more useful to consider just the conversion of PE g to KE without explicitly considering the intermediate step of work. If we release the mass, gravitational force will do an amount of work equal to mgh on it, thereby increasing its kinetic energy by that same amount (by the work-energy theorem). Gravitational potential energy may be converted to other forms of energy, such as kinetic energy. Converting Between Potential Energy and Kinetic Energy The difference in gravitational potential energy of an object (in the Earth-object system) between two rungs of a ladder will be the same for the first two rungs as for the last two rungs. We usually choose this point to be Earth’s surface, but this point is arbitrary what is important is the difference in gravitational potential energy, because this difference is what relates to the work done. Because gravitational potential energy depends on relative position, we need a reference level at which to set the potential energy equal to 0. When it does positive work it increases the gravitational potential energy of the system. The force applied to the object is an external force, from outside the system. An object’s gravitational potential is due to its position relative to the surroundings within the Earth-object system. Why do we use the word “system”? Potential energy is a property of a system rather than of a single object-due to its physical position. For convenience, we refer to this as the PE g gained by the object, recognizing that this is energy stored in the gravitational field of Earth.

This energy is associated with the state of separation between two objects that attract each other by the gravitational force. We define this to be the gravitational potential energy ( PE g)put into (or gained by) the object-Earth system. The work done on the mass is then W = Fd = mgh. If the object is lifted straight up at constant speed, then the force needed to lift it is equal to its weight mg. Let us calculate the work done in lifting an object of mass m through a height h, such as in Figure 1. The work done against the gravitational force goes into an important form of stored energy that we will explore in this section. When there is work, there is a transformation of energy. Show how knowledge of the potential energy as a function of position can be used to simplify calculations and explain physical phenomena.Ĭlimbing stairs and lifting objects is work in both the scientific and everyday sense-it is work done against the gravitational force.Show that the gravitational potential energy of an object of mass m at height h on Earth is given by PE g = mgh.Explain gravitational potential energy in terms of work done against gravity.