Physics Question, I am desperate. Regarding Force Diagrams and Velocity of an object being pulled.

a crate weighing 278 N is being pulled witha a force F=154 N. The rope used to pull the crate makes an angle 32 degrees with the horizontal. The coeffieceint of friction between crate and floor is f=.20. A). What is the magnitude of the work by each of the following individual forces acting on the crate if the crate is pulled a distance of 8 m. Weight? Normal Force? friction? applied force,F? B) What is the crates velocity after being pulled the full distance of 8 m, if its initial velocity was vi=1.2m/s?

A) Work done by
1) weight = 0
2) normal = 0 also

3) find the friction Fr :

Fr = uk (mg - F sin32) = 0.2 (278 - 154 sin32) = 39.28 N opposite to the direction of motion , so its

work would be 39.28 x 8 x cos180 = - 314.24 J

4) the work done by F = F x 8 x cos 32 = 154 x 8 x cos 32 = 983.736 J

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B) find a :

F cos32 - Fr = ma

=> 130.6 - 39.28 = (278 / 9.8) a

=> a = 3.22 m/s^2

usng V2^2 = V1^2 + 2 a d find V2 :

=> V2^2 = (1.2)^2 + 2(3.22) x 8

=> V2 = 7.28 m/s

The work done by friction is the friction force times the distance and the work done by the applied force is the horizontal component of the tension in the rope multiplied by the distance. The normal force is the weight of the crate minus the vertical component of the tension in the rope. The friction force is the normal force times the coefficient of kinetic friction. The difference between the work done by the applied force and the friction force is the amount of kinetic energy the crate has so you just find the velocity using the kinetic energy equation.

There's some hints for ya and there are other ways of doing those problems