Standard +0.3 This is a standard M1 friction problem requiring resolution of forces in two directions and application of F=μR. While it involves multiple steps (resolving vertically for R, then horizontally for T, solving simultaneous equations), it follows a completely routine method with no novel insight required. The 30° angle and fractional coefficient are straightforward to work with, making this slightly easier than the average A-level question.
\includegraphics{figure_1}
A boy is pulling a sledge of mass 8 kg in a straight line at a constant speed across rough horizontal ground by means of a rope. The rope is inclined at 30° to the ground, as shown in Figure 1. The coefficient of friction between the sledge and the ground is \(\frac{1}{5}\).
By modelling the sledge as a particle and the rope as a light inextensible string, find the tension in the rope. [8]
B1 for F = 0.2R or F = µR and µ = 0.2, seen (could just be on a diagram).
First M1 for resolving vertically with correct no. of terms and T resolved (allow
missing g).
First A1 for a correct equation.
Second M1 for resolving horizontally with correct no. of terms and T resolved.
(M0 if there is an ‘ma’ term which does not subsequently disappear.)
Second A1 for a correct equation.
Third ddM1 (dependent on both previous M’s) for producing an equation in T
only.
Fourth dM1 (dependent on previous M) for solving for T
Third A1 for T =16 (N) or 16.2 (N) No other answers.
4(a)
Answer
Marks
ALT
02 11.222gd
d 6.4
max ht. 3.66.410 m
11.22 u22g x 3.6
u 14
02 1422gh
Answer
Marks
h10 m
M1 A1
A1
A1
(4)
M1
A1
A1
A1 (4)
Answer
Marks
(b)
1
10 = gt2
2
10
t
7
10
Total2x 2.9 or 2.86
Answer
Marks
7
M1 A1
A1
dM1 A1
(5)
Answer
Marks
(c)
v
11.2
O 1.1(4) t
Answer
Marks
V
B1 single line
dB1 V < -11.2
B1 11.2
B1 1.1(4)
(4)
13
Notes
4(a)
Answer
Marks
ALT
M1 for a complete method to find d (d = distance from A to top)
First A1 for a correct equation in d only.
Second A1 for d = 6.4
Third A1 for 6.4 + 3.6 = 10 (m)
M1 for a complete method (must have 2nd equation) to find h
First A1 for u = 14
Second A1 for correct 2nd equation
Third A1 for h = 10 (m)
Question 3:
3 | F0.2R
RTsin30o 8g
FTcos30o
0.2(8gTsin30o)Tcos30o
T 16 Nor16.2 N | B1
M1 A1
M1 A1
ddM1
dM1 A1
8
Notes
B1 for F = 0.2R or F = µR and µ = 0.2, seen (could just be on a diagram).
First M1 for resolving vertically with correct no. of terms and T resolved (allow
missing g).
First A1 for a correct equation.
Second M1 for resolving horizontally with correct no. of terms and T resolved.
(M0 if there is an ‘ma’ term which does not subsequently disappear.)
Second A1 for a correct equation.
Third ddM1 (dependent on both previous M’s) for producing an equation in T
only.
Fourth dM1 (dependent on previous M) for solving for T
Third A1 for T =16 (N) or 16.2 (N) No other answers.
4(a)
ALT | 02 11.222gd
d 6.4
max ht. 3.66.410 m
11.22 u22g x 3.6
u 14
02 1422gh
h10 m | M1 A1
A1
A1
(4)
M1
A1
A1
A1 (4)
(b) | 1
10 = gt2
2
10
t
7
10
Total2x 2.9 or 2.86
7 | M1 A1
A1
dM1 A1
(5)
(c) | v
11.2
O 1.1(4) t
V | B1 single line
dB1 V < -11.2
B1 11.2
B1 1.1(4)
(4)
13
Notes
4(a)
ALT | M1 for a complete method to find d (d = distance from A to top)
First A1 for a correct equation in d only.
Second A1 for d = 6.4
Third A1 for 6.4 + 3.6 = 10 (m)
M1 for a complete method (must have 2nd equation) to find h
First A1 for u = 14
Second A1 for correct 2nd equation
Third A1 for h = 10 (m)
\includegraphics{figure_1}
A boy is pulling a sledge of mass 8 kg in a straight line at a constant speed across rough horizontal ground by means of a rope. The rope is inclined at 30° to the ground, as shown in Figure 1. The coefficient of friction between the sledge and the ground is $\frac{1}{5}$.
By modelling the sledge as a particle and the rope as a light inextensible string, find the tension in the rope. [8]
\hfill \mbox{\textit{Edexcel M1 2016 Q3 [8]}}