Question

A running track at Harvard University uses a surface with a force constant of 2.5 ×105N/m This surface is compressed slightly every time a runner's foot lands on it. The force exerted by the foot, according to the Saucony shoe company, has a magnitude of 2700 N for a typical runner.

(a)Treating the track's surface as an ideal spring, find the amount of compression caused by a foot hitting the track.

Answer in cm

(b)Treating the track's surface as an ideal spring, find the energy stored briefly in the track every time a foot lands.

Answer in J

Please help me!!!! Thank you in advance :)

Answer 1

The spring force is given by,

F= -kx

where, F is the exerted force ,k is force constant, x is the compression of spring.

Therefore from above equation you can calculate x,

x= -F/k

x= - 2700 N/(2.5*10^5 N/m)

x= -1.08 cm

b) Energy stoared is,

E= 1/2 kx^2

E= 0.5 *2.5*10^5*(-1.08*10^-2)^2

E = 14.6 J