Standard +0.3 This is a straightforward power-force-velocity problem requiring standard mechanics techniques: resolving forces parallel/perpendicular to the plane, applying P=Fv to find tension, then using equilibrium (constant speed) to find friction coefficient. All steps are routine M1 content with no novel insight required, making it slightly easier than average.
A crate of mass 600 kg is being pulled up a line of greatest slope of a rough plane at a constant speed of \(2\) m s\(^{-1}\) by a rope attached to a winch. The plane is inclined at an angle of \(30°\) to the horizontal and the rope is parallel to the plane. The winch is working at a constant rate of 8 kW.
Find the coefficient of friction between the crate and the plane. [5]
For attempt to resolve parallel to the plane; 3 terms;
allow sign errors; allow sin/cos mix; allow g missing;
F not resolved.
Allow with just DF.
Answer
Marks
Guidance
Use of F =R
DM1
To form an equation in only where R is a
component of weight or mass.
3
=0.192 or
Answer
Marks
Guidance
9
A1
Awrt 0.192 [0.1924500897].
1
Oe, e.g. .
3 3
Allow 2sf.
5
Answer
Marks
Guidance
Question
Answer
Marks
Question 3:
3 | 8000
Driving force = or 4000
2 | B1 | P
Use of F = ,oe. E.g. DF2=8000.
v
R=600gcos30 =3000 3=5196.152423
| B1
their Driving force−600gsin30−F =0
F =4000−3000=1000 | *M1 | For attempt to resolve parallel to the plane; 3 terms;
allow sign errors; allow sin/cos mix; allow g missing;
F not resolved.
Allow with just DF.
Use of F =R | DM1 | To form an equation in only where R is a
component of weight or mass.
3
=0.192 or
9 | A1 | Awrt 0.192 [0.1924500897].
1
Oe, e.g. .
3 3
Allow 2sf.
5
Question | Answer | Marks | Guidance
A crate of mass 600 kg is being pulled up a line of greatest slope of a rough plane at a constant speed of $2$ m s$^{-1}$ by a rope attached to a winch. The plane is inclined at an angle of $30°$ to the horizontal and the rope is parallel to the plane. The winch is working at a constant rate of 8 kW.
Find the coefficient of friction between the crate and the plane. [5]
\hfill \mbox{\textit{CAIE M1 2024 Q3 [5]}}