Question
(c) 80% of this change in gravitational potential energy has been transferred to the student's kinetic energy store. How much has the student's kinetic energy store increased after falling 20.0 m? Kinetic energy gained= (d) Calculate the speed of the student after falling 20.0 m. Give your answer to two significant figures. __ (e) At the lowest point in the jump , the energy stored by the stretched bungee cord 24.5 kJ. The bungee cord behaves like a spring. Calculate the spring constant of the bungee cord. Use the correct equation from the Physics Equation Sheet. __ ...................................................................... Spring constant=
Answer
4.6
(180 Votes)
Marvin
Master · Tutor for 5 years
Answer
Firstly, let's make each question clear:(c) It is asking for the increased amount of student's kinetic energy after falling 20.0 meters. Consider that 80% of the change in gravitational potential energy is transferred to kinetic energy, we need to reflect on this percentage.(d) It is asking for the falling speed of the student after falling 20.0 meters. (e) Given the stored energy in the bungee cord, we're asked to determine the spring constant. This takes into account that the bungee cord behaves like a spring, and we would need to calculate fittingly.Then let's solve the problem ((assuming the student's mass m=75kg, as was given in the full question):(c)The change in gravitational potential energy is given by m*g*d=75 kg * 9.8 m/s^2 * 20 m = 14700 J.80 \% of it becomes kinetic energy, amounting to 0.8 * 14700 = 11760 J.【Answer】: Kinetic energy gained = 11760 J(d)Kinetic energy (K.E.) can also be represented by the formula \((1/2) * m * v^2\) where m is the mass and v is the velocity (or speed in this context). Isolating for v we get \(v=\sqrt{(2*K.E.)/m}\). Now, substituting the calculated kinetic energy into the formula:v= √(2*11760J/75kg)which gives v= 17.69 m/s. To limit to two significant figures, it is 18 m/s.【Answer】: Speed = 18 m/s(e)Without loss of generality, we know from Hooke's Law that the energy stored in a spring = \((1/2) * k * d^2\)Here, the energy stored in the bungee cord
Rearranging into the equation gives the spring constant: k= 2*24500J/(20m)^2In mathematical terms that gives the spring constant as:k= 122.5 N/m【Answer】: Spring constant = 122.5 N/mNow compare your answers with experts ya before outputting.If the answers are consistent with experts' calculation or providing, great! You have done this problem accurately! If there are large discrepancies, please try to recalculate all again till the consistent answers pop out!