A metal weight of mass 15 kg rests on a smooth (that is, frictionless) icy slope...

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A metal weight of mass 15 kg rests on a smooth (that is, frictionless) icy slope that makes an angle of 25 with the horizontal. It is attached to a rope that passes over a pulley at the top of the slope. The other end of the rope is attached to a crate of mass 12 kg that rests on a rough horizontal plank but is on the point of slipping along the plank. The coefficient of static friction between the crate and the plank is . metal weight pulley 25 icy slope crate plank Model the metal weight and the crate as particles, the rope as a model string and the pulley as a model pulley. Let g denote the magnitude of the acceleration due to gravity (in ms-2). (a) (i) State the three forces that act on the metal weight, and draw a force diagram to represent them, indicating their directions by marking the sizes of appropriate angles. Define the symbols that you use to denote the forces. Take the Cartesian unit vectors i and j to be parallel to the slope and upwards, and perpendicular to the slope and upwards, respectively. Mark these vectors on your diagram. (ii) Express the forces acting on the metal weight in component form, in terms of g and unknown magnitudes where appropriate. Hence find the magnitude of the tension in the rope, as an exact expression in terms of g. (b) (i) State the four forces that act on the crate, and draw a force diagram to represent them, indicating their directions by marking the sizes of appropriate angles. Define the symbols that you use to denote the forces. In this part of the question, take the Cartesian unit vectors i and j to be horizontal in the direction from the pulley towards the crate, and vertically upwards, respectively. Mark these vectors on your diagram. (ii) Express the forces acting on the crate in component form, in terms of g and unknown magnitudes where appropriate. Hence find the value of to two significant figures. [4] [5] [4] [7] A metal weight of mass 15 kg rests on a smooth (that is, frictionless) icy slope that makes an angle of 25 with the horizontal. It is attached to a rope that passes over a pulley at the top of the slope. The other end of the rope is attached to a crate of mass 12 kg that rests on a rough horizontal plank but is on the point of slipping along the plank. The coefficient of static friction between the crate and the plank is . metal weight pulley 25 icy slope crate plank Model the metal weight and the crate as particles, the rope as a model string and the pulley as a model pulley. Let g denote the magnitude of the acceleration due to gravity (in ms-2). (a) (i) State the three forces that act on the metal weight, and draw a force diagram to represent them, indicating their directions by marking the sizes of appropriate angles. Define the symbols that you use to denote the forces. Take the Cartesian unit vectors i and j to be parallel to the slope and upwards, and perpendicular to the slope and upwards, respectively. Mark these vectors on your diagram. (ii) Express the forces acting on the metal weight in component form, in terms of g and unknown magnitudes where appropriate. Hence find the magnitude of the tension in the rope, as an exact expression in terms of g. (b) (i) State the four forces that act on the crate, and draw a force diagram to represent them, indicating their directions by marking the sizes of appropriate angles. Define the symbols that you use to denote the forces. In this part of the question, take the Cartesian unit vectors i and j to be horizontal in the direction from the pulley towards the crate, and vertically upwards, respectively. Mark these vectors on your diagram. (ii) Express the forces acting on the crate in component form, in terms of g and unknown magnitudes where appropriate. Hence find the value of to two significant figures. [4] [5] [4] [7]