A 1kg spring has an unloaded length 10cm and has an elastic constant of 100N/m. It is compressed to 6cm then placed facing upwards on the floor. When released it travels vertically upwards. How high does it jump? You may assume no energy is lost to heat o
This may at first look like a horrible SUVAT problem, but it is actually testing your ability to calculate energy transfers. It is helpful for these questions to first draw a diagram then work out what energy transfers are taking place. (Even if the diagram is unhelpful in calculation, it will help you to visualise the scenario.) In this case because the spring is being compressed, it now has Elastic Potential Energy. When the spring is released, this energy is converted into Kinetic Energy. The assumptions tell us no energy is lost in the transfers, so the Elastic Potential Energy must equal Kinetic Energy. When the spring is as the highest point of its jump, it will have no kinetic energy as at this point, it will not be moving (just for a split second). Therefore we know all of its Kinetic Energy must have been transferred to Gravitational Potential Energy. We said earlier that the Kinetic Energy at the point of release was equal to the Elastic Potential Energy therefore the Elastic Potential Energy must equal the Gravitational Energy at the highest point.
The equation for Elastic Potential Energy Is E= 1/2 x k x ΔL2 where E is Energy, k is the elastic constant and ΔL is the change in length of the spring when compressed. From the question we can extract the relevant numbers to calculate E: k=100N/m and ΔL = 10cm – 6cm = 4cm which we can convert to metres by dividing by 100 to get ΔL = 0.04m. Type the numbers into a calculator to get E = 2J. Finally, the equation for gravitational potential energy is E = m x g x h which we can rearrange to get height (h) as the subject: h = E / (m x g). m is mass (1kg) and g is gravity on earth which is always 9.81m/s2 (this will be on any formula sheet). Use the E we worked out earlier and the values of m and g given to calculate h by typing these into a calculator using the rearranged equation to get height = 0.204m
