Question 6 20 marks You should be able to answer this question after studying Unit 5. A crate of mass 17 kg rests on a rough ramp inclined at an angle of 20 to the horizontal. A rope attached to the crate runs at an angle of 10 to the ramp and passes over a pulley suspended above the top of the ramp, as shown in the diagram below. A metal ball hangs freely from the other end of the rope. The rope remains taut. The coefficient of static friction is 0.21. The crate is at rest, but is on the point of slipping up the ramp. rope _ 10 ball crate 20 Take the magnitude of the acceleration due to gravity to be g = 9.8ms-2. Model the crate and the ball as particles, the rope as a model string and the pulley as a model pulley. (a) State the four forces that act on the crate and draw a force diagram showing them, including angles that show their directions [5] (b) Take the unit vector i to be in the direction up the ramp and the unit vector j to be in the direction perpendicular to the ramp and upwards. Express the forces in component form, in terms of unknown magnitudes where appropriate. Hence find the magnitude of the tension in the rope in newtons to two significant figures. [12] (c) By considering the forces acting on the ball, find the mass of the ball in kilograms to two significant figures. [3]