You build a t-shirt launcher for basketball games using a compressible spring. The mass of the t-shirt is 0.16 kg. The spring has a stiffness 250 N/m, and its unstretched length is 0.6 m. To launch a t-shirt, you hold a shirt in your hand, use it to push it down on the spring until the spring’s length is 0.2 m, and then you latch the spring to hold it at rest before the launch. A picture of the spring and t-shirt is shown below. Figure A shows the spring when it is relaxed. Figure B shows the partially compressed spring as you are pushing it downward, and Figure C shows the spring when it is fully compressed. (The picture is not drawn to scale.) You can assume you push it downward at constant speed.
(a) How much work did you do on the spring in order to compress the spring?
W = J
(b) To launch a second t-shirt, you repeat the procedure but this time you compress the spring only half as much (so its compressed length is 0.4 m). In this case, how much work did you do on the spring in order to compress the spring?
W = J
