5.1

A force is nonconservative if the work it does/done on an object which is moving between two points depends on the path taken.
Or
A force is nonconservative if the work it does/done in moving an object around a closed path is nonzero.
Tip: a nonconservative force does not change the mechanical energy of a system.

2 marks
(1 x 2 marks)

5.2

Option 1
Any one ^{(1)}
^{(2 + 3 + 4) }
^{(5)}
Tips:
 The crate starts from rest and accelerates up the slope.
 It helps to draw a freebody diagram to show all of the forces acting on an object in order to identify which of the forces do the work.
 In this case, negative work is done against gravity and friction. Positive work is done by the tension in the rope. Using the formula W = FΔxcosθ, calculate the work done by each of the forces acting on the crate.
 The work done by the frictional force is equal to W_{f} = (13,5)(15,6)cos 180°
 The work done against gravity is equal to W_{g} = (20)(9,8)(15,6sin18°)cos180°
 The work done by the tension is equal to W_{T} = (96,8)(15,6)cos0°
 The normal force does no work since the normal force acts perpendicularly to the direction of the displacement.
 Using the workenergy theorem W_{net} = ΔE_{k}
There are more ways to answer this question. To view other options, click here.

5 marks
(5 x 1 mark)
Marking criteria:
 ^{(1) }Any one of the correct equation
 ^{(2) }Correct substitution for work done by gravity or ΔE_{p }
 ^{(3) }Correct substitution for work done by motor and friction
 ^{(4) }Correct substitution for ∆E_{k }
 ^{(5) }Correct final answer: 5,96 m·s^{1 }

5.3

Option 1
^{(1)}
^{(2)}
^{(3)}
Tips:
 The average power is the product of the applied force of the motor and the average velocity of the crate.
 Since the crate accelerates uniformly from rest to a speed of 5,96 m·s^{1}, the average speed is the average of these two velocities.
There are more ways to answer this question. To view other options, click here.

3 marks
(3 x 1 mark)
Marking criteria:
 ^{(1) }Correct equation for power
 ^{(2) }Correct substitution into power equation
 ^{(3) }Correct final answer: 288,46 W
 Range: 286,46 W to 288,73 W

5.4

Tips:
 Although older papers may indicate that you may also use components in freebody diagrams, they will no longer be marked be awarded the marks.
 Do not resolve the weight into parallel and perpendicular components in any freebody diagram.
N 
F_{N}/196N/normal/F_{normal} 
f 
(kinetic) friction/F_{f}/F_{w}/f_{k} 
w 
F_{g}/F_{w}/weight/mg/gravitational force/F_{Earth on crate} 

3 marks
(3 x 1 mark)

5.5

How to approach this question:
 If upwards is taken as the positive direction.
 When the rope breaks, the crate continues to move up the slope but slows down until it comes to rest at point D. Then, it slides down the slope with a less steep gradient because friction and gravity act in opposite directions.
Or
 If upwards is considered as negative.

4 marks
(4 x 1 mark)
Marking criteria:
 The first straight line starts at zero with a positive gradient, reaching a maximum
velocity.
 A second straight line with the negative gradient from maximum velocity to zero.
 The third straight line continues from the second line at zero and extends below the xaxis.
 The third line has a smaller negative gradient than the second line.
