Additional Answer Options: 5.3

5.1

A force is non-conservative if the work it does/done on an object which is moving between two points depends on the path taken.

Or

A force is non-conservative if the work it does/done in moving an object around a closed path is non-zero. 

Tip: a non-conservative 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 free-body 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 work-energy 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 free-body diagrams, they will no longer be marked be awarded the marks.
• Do not resolve the weight into parallel and perpendicular components in any free-body diagram. 

N	FN/196N/normal/Fnormal
f	(kinetic) friction/Ff/Fw/fk
w	Fg/Fw/weight/mg/gravitational force/FEarth 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 x-axis.
• The third line has a smaller negative gradient than the second line.