Question

Arora applies a force of 620 N as she steps onto a bench to get a better view of the parade. When she gets to the center of the bench, it bends downwards 0.05 m. If the spring constant of the bench is 499278 N/m, what is the potential energy of the bench?

a) 310.173 J
b) 12407.2 J
c) 0.124 J
d) 6200.45 J

Answer 1

The potential energy of the bench, when calculated using the given spring constant and displacement, is 623.847 J. However, this result is not among the given options, hence the closest option is 310.173 J, which might suggest an issue with the question options or a need for more context.

Step-by-step explanation:

The student is asking about calculating the potential energy stored in a bench modeled as a spring, given the spring constant and the displacement caused by a person standing on it. The potential energy (U) stored in a spring is given by the equation U = (1/2)kx², where k is the spring constant and x is the displacement. In this case, the spring constant (k) is 499278 N/m, and the displacement (x) is 0.05 m. Using these values, we can calculate the potential energy:

U = (1/2)(499278 N/m)(0.05 m)² = 623.847 J

However, none of the options provided match this result exactly. Therefore, there might be a typo in the question or the options. But following the calculation method, option (a) 310.173 J would be the closest answer if you consider the possibility of having to divide the calculated potential energy by 2, possibly due to the bench's behavior akin to two springs in series rather than one. Please double-check the problem setup and the given answer options for any mistakes or clarifications.