6.2. Energy http://www.ck12.org
Answer:A spring constant of 200 N/m is understood to mean that it requires a force of 200 N to stretch or compress
the spring 1 meter. A spring constant of 100 N/m requires half the force (100 N) to stretch or compress the spring
the same distance, 1 meter.
2a. The force required to stretch a spring 10 cm is 20 N. What force is needed to stretch the spring 20 cm?
Answer: Since the force is directly proportional to the distance the spring is stretched, twice the force must be
applied to stretch the spring 20 cm or 40 N.
2b. What is the value of the spring constant,kof the spring?
Answer:F=kx: 20=k( 0. 10 ),k= 200 N/m
2c. What is the energy stored in the spring when it is stretched 10 cm?
Answer:PE=^12 kx^2 =^12 ( 200 )( 0. 10 )^2 = 1. 0 J
2d. What is the energy stored in the spring if it is stretched another 10 cm?
Answer:PE=^12 kx^2 =^12 ( 200 )( 0. 20 )^2 = 4. 0 J. Notice, by reviewing (2c) and (2d) that thePEis directly propor-
tional to the square of the distance.