Question

Resistance bands are long elastic band type of devices that may be used as part of a weight-lifting regimen. One such band has an unstretched length of 4 ft. An athlete who can exert 33 lb of force finds that she can stretch the band to 5.5 ft (that is, 1.5 ft longer than its unstretched length).

1. Determine Hooke's constant of the band. Round the final answer to the nearest whole number. Give answer in lb/ft

2. Calculate the energy exerted by the athlete into the band. Round the final answer to the nearest whole number. Give answer in Joules.

Answer 1

the force for such a system is gievn by the Hookes law as

F = k*x

where,

k = spring constant/hookes constant

x = change in the length of the band = 5.5 -4.0 = 1.5 ft

therefore

33 = k*(1.5)

or k = 33 lb/1.5ft = 22 lb/ft

2) the energy exerted by the athlete is equal to the work done by the athlete

substitutung the values, we get

E = k*x²/2 = (22)(1.5)²/2 = 24.75 ft-lb

we know that

1 ft-lb = 1.3558 joules

therefore 24.75 ft-lb = 1.3558 x 24.75 joules = 33.56 = 34 joules