1. A 31 kg crate full of fruits is placed on an incline that is17â—¦ below the horizontal. The crate is connected to a spring thatis anchored to a vertical wall, such that the spring is parallel tothe surface of the incline.

(a) If the crate was connected to the spring at equilibriumlength, and then allowed to stretch the spring until the cratecomes to rest, determine the spring constant. Assume that theincline is frictionless and that the change in length of the springis 2.13 m.

(b) If there is friction between the incline and the crate,would the spring stretch more, or less than if the incline isfrictionless? You must use concepts pertaining to work andenergy.

2. David is running with a horizontal velocity, along levelground. While running, he encounters a 2.51 m vine of negligiblemass; the vine was hanging vertically from a tall tree limb and theend of the vine is directly level with his center of mass. Daviddecides to grab the vine and swing, because he loves experiencinguniform circular motion. At the maximum height, David takes mentalnote that the angle the vine makes with the vertical is 21o .Ignore any elastic properties the vine may have.

(a) At the instant David grabs the vine, he is undergoingcircular motion. Identify the external force on David that issupplying the centripetal force for his motion.

(b) Determine David’s centripetal acceleration.
(c) Determine the magnitude of the external force identified above,at the beginning of the swing.