We know from the reading that it is possible to move the same object two different distances and still do the same amount of work. Let's consider an example in which Jane pushes a block of ice up an incline while Kip lift the same block of ice vertically to the top of the same incline. See the figure below. (look at picture) We will assume that there is no friction between the surface of the incline and the block of ice. Both of these situations will require the same amount of work and that the result of lifting the ice block to some height imparts potential energy to the ice. In this activity, we will make various calculation to help us better understand the relationship between work and potential energy and the idea of conservation of energy. For this activity we will assume that the mass of the ice block is 5.6 kg and the vertical height of the incline is 2 m. This is the vertical distance that Kip must lift the block of ice. We will assume that the acceleration due to gravity is 10 m/s2. Consider the following questions.
We know from the reading that it is possible to move the same object two different distances and still do the same amount of work. Let's consider an example in which Jane pushes a block of ice up an incline while Kip lift the same block of ice vertically to the top of the same incline. See the figure below. (look at picture)
We will assume that there is no friction between the surface of the incline and the block of ice. Both of these situations will require the same amount of work and that the result of lifting the ice block to some height imparts potential energy to the ice. In this activity, we will make various calculation to help us better understand the relationship between work and potential energy and the idea of conservation of energy. For this activity we will assume that the mass of the ice block is 5.6 kg and the vertical height of the incline is 2 m. This is the vertical distance that Kip must lift the block of ice. We will assume that the acceleration due to gravity is 10 m/s2. Consider the following questions.
(a) What is the weight of the block of ice?
w = Fg = 56 N
(b) Since Kip must lift this weight a distance of 2 m, he must apply a force that is equal to the weight. How much work does Kip do as he lifts the block of ice?
W = F d = 112 J
(c) The work that is done by Jane is exactly the same as the work done by Kip; however, the incline has a length of 5.5 m. Jane must push her block of ice a total distance of 5.5 m up the incline. Knowing the work done by Jane is the same as the work done by Kip found in part (b), calculate the force that she must apply to push the ice block up the incline.
F = 20.36 N
An incline is one example of a simple machine. Although Jane is doing the same amount of work as Kip, she is applying less force over a greater distance.
(d) Once the blocks are placed on the top of the incline, they have stored energy in the form of potential energy. For either block, what is the potential energy at the top of the incline?
PE = 112 J
(e) Suppose that once Jane reaches the top of the incline she decides to let the the ice block slide back down to the bottom. As the block slides down, the potential energy that it had at the top is being converted into kinetic energy at the bottom. Once the block reaches the bottom all of the potential energy that it had at the top has been converted into kinetic energy. Using your answer from part (d) for PETOP and the fact that KEBOTTOM = PETOP, find the speed of the ice block as it reaches the bottom? You will need to use the definition of kinetic energy KE = 1/2 m v2. The speed of the ice block at the bottom of the incline is
vBOTTOM = ____ m/s
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