Question

1. A 31 kg crate full of fruits is placed on an incline that is 17◦ below the horizontal. The crate is connected to a spring that is anchored to a vertical wall, such that the spring is parallel to the surface of the incline.

(a) If the crate was connected to the spring at equilibrium length, and then allowed to stretch the spring until the crate comes to rest, determine the spring constant. Assume that the incline is frictionless and that the change in length of the spring is 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 is frictionless? You must use concepts pertaining to work and energy.

2. David is running with a horizontal velocity, along level ground. While running, he encounters a 2.51 m vine of negligible mass; the vine was hanging vertically from a tall tree limb and the end of the vine is directly level with his center of mass. David decides to grab the vine and swing, because he loves experiencing uniform circular motion. At the maximum height, David takes mental note 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 undergoing circular motion. Identify the external force on David that is supplying 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.

Answer 1