(iii) How much work does the frictional force do on the cabinet? (2 marks) (iv) How much work does the mg and N do on the cabinet? ( 2 marks) (v) What is the total work done on the cabinet by all the forces that act on it? (2 marks) (b) A crate whose mass m is 15 kg is pulled a distance d (=5.7m) up a frictionless ramp to a height h of 2.5 m. (i) What Force F must the winch cable exert? (3 marks) (ii)How much work is done by the force F? (3 marks) (iii) How much work would be required to lift the crate vertically upward, through the height h?

(iii) The work done by the frictional force on the cabinet is given by the formula:<br /><br />Work = Force x Distance x cos(θ)<br /><br />where Force is the frictional force, Distance is the distance the cabinet moves, and θ is the angle between the force and the direction of motion.<br /><br />(iv) The work done by the gravitational force (mg) and the normal force (N) on the cabinet is zero, as they are perpendicular to the direction of motion.<br /><br />(v) The total work done on the cabinet by all the forces acting on it is the sum of the work done by each individual force. In this case, it would be the sum of the work done by the frictional force and the work done by the gravitational force and the normal force.<br /><br />(b) (i) The force F that the winch cable must exert can be calculated using the formula:<br /><br />F = m x g x sin(θ)<br /><br />where m is the mass of the crate, g is the acceleration due to gravity, and θ is the angle of the ramp.<br /><br />(ii) The work done by the force F is given by the formula:<br /><br />Work = F x d x cos(θ)<br /><br />where F is the force exerted by the winch cable, d is the distance the crate is pulled up the ramp, and θ is the angle between the force and the direction of motion.<br /><br />(iii) The work required to lift the crate vertically upward through the height h is given by the formula:<br /><br />Work = m x g x h<br /><br />where m is the mass of the crate, g is the acceleration due to gravity, and h is the height the crate is lifted.