Al dl (a) What is the equivalent spring constant of the bow? N/m (b) How much work is done in pulling the bow?

A 13.8 kg crate is pulled up a rough inclinewith an initial speed of 1.5 m/s. The pullingforce is 123.0 N parallel to the incline, whichmakes an angle of 13.6◦ with the horizontal. The coefficient of kinetic friction is 0.33 andthe crate is pulled a distance of 7.8 m.The acceleration of gravity is 9.81 m/s^2a) Find the work done by Earth’s gravityon the crate.Answer in units of J.b) Find the work done by the force of frictionon the crate.Answer in units of J.c) Find the work done by the puller on thecrate.Answer in units of J.d) Find the change in kinetic energy of thecrate.Answer in units of J. e) Find the speed of the crate after it is pulled7.8 m.Answer in units of m/s.

The spring is unstretched at the position x = 0. Under the action of a force P, the cart moves from the initial position x1 = -6 in. to the final position x2 = 3 in. Determine (a) the work done on the cart by the spring and (b) the work done on the cart by its weight. Unstretched position 3 lb/in. 14 lb wwww 15°

An archer using a simple bow exerts a force of 165 N to draw back the bow string 0.51 m. (Assume the given force is the force exerted at the very end of the pull.) (a) What is the total work (in J) done by the archer in preparing to launch her arrow? (Hint: Compute the total work as: total work = Fanal - Finitia ld.) Ffinal (b) If all the work is converted into the kinetic energy of the arrow upon its release, what is the arrow's speed (in m/s) as it leaves the bow? Assume the mass of the arrow is 0.021 kg and ignore any kinetic energy in the bow as it relaxes to its original shape. m/s (c) If the arrow is shot straight up, what is the maximum height (in m) achieved by the arrow? Ignore any effects due to air resistance in making your assessment. (Assume the arrow is initially 2 m from the ground.)