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SITEMAP School Physics Notes: Forces Section 4.5 Elastic potential energy calculations
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Forces 4: 4.5 Elastic potential energy formula, energy stored, work done , calculations, problem solving Doc Brown's Physics exam study revision notes Sub-index of physics notes on FORCES section 4 Elastic potential energy This page contains online questions only. Jot down your answers and check them against the worked out answers at the end of the page 4.5a Elastic potential energy - energy stored and work done - calculations
This equation is only valid within the limit of proportionality, that is when the spring obeys Hooke's Law.
Using the experiment results from above we can calculate the stored elastic potential energy for the 0.06 m extension of the spring with a load of 3.0 N. You can actually do this calculation in two ways. (a) Using the equation E_{e} = ^{1}/_{2} k e^{2} described above k = 50 N/m, e = 0.06 m E_{e} = 0.5 x 50 x 0.06^{2} = 0.09 J
BUT, you can also do the stored energy calculation from the graph of results using the graph above and the principle explained by the graph below.
(b) Calculating the area under the graph of force versus extension. This is the area under the shaded triangle of the graph of force versus extension. Using the same values as above: x = 0.06 m, y = 3.0 N area under graph = xy / 2 E_{e} = 0.06 x 3.0 / 2 = 0.09 J Comments on the above two calculations:
Remember, force must be in newtons and extension in metres (cm/100 = m, mm/1000 = m). At a higher mathematical level what you are doing via the graph is called an integration, here of the work equation W = F x d. BUT, you cannot use this simple equation to calculate the stored energy because for this equation to be valid the force must be constant, but for a spring the force must be steadily increased to increase the extension so please use E_{e} = ^{1}/_{2} k e^{2} to calculate elastic potential energy unless given sufficient graphical data! 4.5b Questions on spring extension and elastic potential energy (overlap with energy 0b, need some graph based questions) Q1A student carried out an experiment by putting weights on the end of a spring.
Q2 A spring is fixed firmly in a vertical position. When a mass of 120.0 g is attached to the spring it extends in length by 3.2 cm.
Q3 A spring with spring constant of 5.00 N/m is stretched for an extra 10.0 cm.
Q4 A spring has a spring constant of 2000 N/m.
Q5 It takes 5.0 J of work to stretch a spring 20 cm.
Q6 A spring stores an extra 20 J of elastic potential energy when stretched an extra 40 cm.
Q7 A stretched string has a total length of 60 cm and a spring constant of 240 N/m.
Q8 A spring has a spring constant of 20.0 N/m.
Q9 For this question you need to know the formula for gravitational potential energy (GPE) and gravitational field constant g = 9.8 m/s^{2} or 9.8 N/kg). Watch out for units, remember in the end to work in J, m and kg.
Sub-index of physics notes: FORCES 4. Elastic potential energy Keywords, phrases and learning objectives for elastic potential energy
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ANSWERS
to calculation questions on elastic potential energy Q1A student carried out an experiment by putting weights on the end of a spring.
Q2 A spring is fixed firmly in a vertical position. When a mass of 120.0 g is attached to the spring it extends in length by 3.2 cm.
Q3 A spring with spring constant of 5.00 N/m is stretched for an extra 10.0 cm.
Q4 A spring has a spring constant of 2000 N/m.
Q5 It takes 5.0 J of work to stretch a spring 20 cm.
Q6 A spring stores an extra 20 J of elastic potential energy when stretched an extra 40 cm.
Q7 A stretched string has a total length of 60 cm and a spring constant of 240 N/m.
Q8 A spring has a spring constant of 20.0 N/m.
Q9 For this question you need to know the formula for gravitational potential energy (GPE) and gravitational field constant g = 9.8 m/s^{2} or 9.8 N/kg). Watch out for units, remember in the end to work in J, m and kg.
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