Resolving Forces

1. A weight of 50.0 N is suspended from a beam by a string. Calculate the horizontal force must be applied to the weight to keep the string at an angle of 40° to the vertical. 65.3N  Calculate the tension in the string. 
2. A weight of 20 N rests on a plane inclined at 40° to the horizontal. Calculate the components of the weight parallel to the plane and perpendicular to the plane.12.86N, 15.32N
3. A weight of 4.33 N is suspended by a string fastened at its upper end. A horizontal force is applied to the weight so that the string makes an angle of 30⁰ with the vertical. Calculate the force and the tension in the string.2.50N, 5.00N
4. A 10 N weight rests on a smooth inclined plane. A force of 5N parallel to the plane is needed to prevent the weight slipping down the plane. Calculate the reaction of the plane and the angle the plane makes with the horizontal.8.66N ,30⁰
5. A garden roller of weight 800 N is being pulled along by a force of 200 N at 40° to the ground. Calculate (a) the force pulling the roller forwards, 153.2N(b) the vertical force exerted by the roller on the ground. 671.4 N
6. Calculate the forces (a) 153.2N and (b) 928.6N in the previous problem if the roller is being pushed instead of being pulled.