| Exam Board | Edexcel |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2016 |
| Session | January |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Forces, equilibrium and resultants |
| Type | Connected particles via tow-bar on horizontal surface |
| Difficulty | Moderate -0.3 This is a standard M1 mechanics problem requiring application of Newton's second law to two connected bodies. While it involves multiple steps and two separate force equations, the method is routine and well-practiced: identify forces, apply F=ma to each body separately, and solve. The conceptual demand is low (standard connected particles setup) and the algebra is straightforward, making it slightly easier than average for A-level. |
| Spec | 3.03c Newton's second law: F=ma one dimension3.03k Connected particles: pulleys and equilibrium |
| Answer | Marks |
|---|---|
| 1(a) | For truck: D6004002400 x 0.5 |
| D2200N | M1 A1 |
| Answer | Marks |
|---|---|
| (b) | For both: D600(M 2400) x 0.5 (or trailer: 600 - 200 = M x0.5) |
| M 800 M 800 | M1 A1 |
| Answer | Marks | Guidance |
|---|---|---|
| (c) | Truck and trailer have same acceleration. | B1 (1) |
| Answer | Marks |
|---|---|
| 1(a) | M1 for NL2 for truck only (or for a complete method if they find M first), with |
| Answer | Marks |
|---|---|
| 1(b) | M1 for NL2 for whole system or trailer only, with correct no. of terms. |
| Answer | Marks |
|---|---|
| 1(c) | B0 if extras included. E.g if ‘tension is same’ is included. |
| Answer | Marks |
|---|---|
| (b) | ForP: 33mu2m(v 4u) |
| Answer | Marks |
|---|---|
| Q | M1 A1 |
Question 1:
--- 1(a) ---
1(a) | For truck: D6004002400 x 0.5
D2200N | M1 A1
A1 (3)
(b) | For both: D600(M 2400) x 0.5 (or trailer: 600 - 200 = M x0.5)
M 800 M 800 | M1 A1
A1 (3)
(c) | Truck and trailer have same acceleration. | B1 (1)
7
Notes
Can mark (a) and (b) ‘together’ if it helps the candidate, provided no wrong working
seen.
1(a) | M1 for NL2 for truck only (or for a complete method if they find M first), with
correct no. of terms, in D only. (M0 if 600 or 400 is replaced by 200)
First A1 for a correct equation .
Second A1 for 2200 (N).
.
--- 1(b) ---
1(b) | M1 for NL2 for whole system or trailer only, with correct no. of terms.
First A1 for a correct equation. (Allow ‘D’ or their D)
Second A1 for 800.
N.B. In both parts of this question use the mass which is being used in their
equation to guide you as to which part of the system is being considered.
--- 1(c) ---
1(c) | B0 if extras included. E.g if ‘tension is same’ is included.
B1 Must include ‘truck and trailer’ or ‘both particles’ or ‘accln is same throughout
the system’
B0 for ‘accln is same’
2(a)
(b) | ForP: 33mu2m(v 4u)
5 P
v 0.7u due E
P
ForQ: 33mu3m(v u)
5 Q
v 1.2u due E
Q | M1 A1
dM1 A1 (4)
M1 A1
dM1 A1 (4)
NotesA truck of mass 2400 kg is pulling a trailer of mass $M$ kg along a straight horizontal road. The tow bar, connecting the truck to the trailer, is horizontal and parallel to the direction of motion. The tow bar is modelled as being light and inextensible. The resistance forces acting on the truck and the trailer are constant and of magnitude 400 N and 200 N respectively. The acceleration of the truck is 0.5 m s$^{-2}$ and the tension in the tow bar is 600 N.
\begin{enumerate}[label=(\alph*)]
\item Find the magnitude of the driving force of the truck. [3]
\item Find the value of $M$. [3]
\item Explain how you have used the fact that the tow bar is inextensible in your calculations. [1]
\end{enumerate}
\hfill \mbox{\textit{Edexcel M1 2016 Q1 [7]}}