Moderate -0.5 This is a straightforward work-energy question requiring resolution of forces on an inclined plane and applying W = Fd. The constant speed simplifies the problem (no acceleration), and the calculation involves standard components: weight down slope (50g sin 60°), resistance (100 N), and distance (5 m). Slightly easier than average due to being a direct application of formulas with no problem-solving insight required.
A winch operates by means of a force applied by a rope. The winch is used to pull a load of mass 50 kg up a line of greatest slope of a plane inclined at 60° to the horizontal. The winch pulls the load a distance of 5 m up the plane at constant speed. There is a constant resistance to motion of 100 N.
Find the work done by the winch. [3]
Force exerted by winch =50gsin60+100 =433.0+100=533.0
M1
For resolving forces along the plane
Work done =5×( 50gsin60+100 )
M1
Use of WD = Force × distance
Work done = 2670 J
A1
Alternative method for Question 1
Answer
Marks
Guidance
PE increase =50g×5sin60
M1
Correct dimensions
Work done =50g×5sin60+100×5
M1
Apply the work-energy equation, 3 terms
Work done = 2670 J
A1
3
Answer
Marks
Guidance
Question
Answer
Marks
Question 1:
1 | [ ]
Force exerted by winch =50gsin60+100 =433.0+100=533.0 | M1 | For resolving forces along the plane
Work done =5×( 50gsin60+100 ) | M1 | Use of WD = Force × distance
Work done = 2670 J | A1
Alternative method for Question 1
PE increase =50g×5sin60 | M1 | Correct dimensions
Work done =50g×5sin60+100×5 | M1 | Apply the work-energy equation, 3 terms
Work done = 2670 J | A1
3
Question | Answer | Marks | Guidance
A winch operates by means of a force applied by a rope. The winch is used to pull a load of mass 50 kg up a line of greatest slope of a plane inclined at 60° to the horizontal. The winch pulls the load a distance of 5 m up the plane at constant speed. There is a constant resistance to motion of 100 N.
Find the work done by the winch. [3]
\hfill \mbox{\textit{CAIE M1 2021 Q1 [3]}}