| Exam Board | Edexcel |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2018 |
| Session | October |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Newton's laws and connected particles |
| Type | Car towing trailer, horizontal |
| Difficulty | Moderate -0.3 This is a standard M1 connected particles question requiring straightforward application of Newton's second law. Part (a) uses F=ma on the whole system to find R, part (b) considers forces on just the car to find tension, and part (c) applies F=ma on an incline with a given sin value. All steps are routine with no problem-solving insight required, making it slightly easier than average. |
| Spec | 3.03b Newton's first law: equilibrium3.03c Newton's second law: F=ma one dimension3.03d Newton's second law: 2D vectors3.03k Connected particles: pulleys and equilibrium3.03l Newton's third law: extend to situations requiring force resolution |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| \(2560 \times 0.4 = 2100 - 640 - R\) | M1A1 | M1 for equation of motion, dimensionally correct with correct no. of terms, condone sign errors in \(R\) only |
| \(R = 436\) ✱ GIVEN ANSWER | A1* | (3) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| Truck: \(1600 \times 0.4 = 2100 - 640 - T\) OR car: \(960 \times 0.4 = T - 436\) | M1A1 | M1 for equation of motion, dimensionally correct, condone sign errors, for either truck or car in \(T\) only |
| \(T = 820\) N | A1 | (3) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| \(2560a' = 2100 - 640 - 436 + 1600g\sin\alpha + 960g\sin\alpha\) | M1A1A1 | M1 for equation of motion in \(a'\) only, dim correct with correct no. of terms, condone sign errors and missing \(g\)'s; -1 each error (omission of \(g\) is one error); if both weight components negative, treat as one error |
| \(a' = 1.05\) or \(1.1\) m s\(^{-2}\) | A1 | A1 for 1.05 or 1.1. N.B. if \(T = 820\) just assumed, M0 |
# Question 7:
## Part (a):
| Answer/Working | Marks | Guidance |
|---|---|---|
| $2560 \times 0.4 = 2100 - 640 - R$ | M1A1 | M1 for equation of motion, dimensionally correct with correct no. of terms, condone sign errors in $R$ only |
| $R = 436$ ✱ GIVEN ANSWER | A1* | (3) |
## Part (b):
| Answer/Working | Marks | Guidance |
|---|---|---|
| Truck: $1600 \times 0.4 = 2100 - 640 - T$ **OR** car: $960 \times 0.4 = T - 436$ | M1A1 | M1 for equation of motion, dimensionally correct, condone sign errors, for either truck or car in $T$ only |
| $T = 820$ N | A1 | (3) |
## Part (c):
| Answer/Working | Marks | Guidance |
|---|---|---|
| $2560a' = 2100 - 640 - 436 + 1600g\sin\alpha + 960g\sin\alpha$ | M1A1A1 | M1 for equation of motion in $a'$ only, dim correct with correct no. of terms, condone sign errors and missing $g$'s; -1 each error (omission of $g$ is one error); if both weight components negative, treat as one error |
| $a' = 1.05$ or $1.1$ m s$^{-2}$ | A1 | A1 for 1.05 or 1.1. N.B. if $T = 820$ just assumed, M0 | (4) **[10]** |
---7. A truck of mass 1600 kg is towing a car of mass 960 kg along a straight horizontal road. The truck and the car are joined by a light rigid tow bar. The tow bar is horizontal and is parallel to the direction of motion. The truck and the car experience constant resistances to motion of magnitude 640 N and $R$ newtons respectively. The truck's engine produces a constant driving force of magnitude 2100 N . The magnitude of the acceleration of the truck and the car is $0.4 \mathrm {~ms} ^ { - 2 }$.
\begin{enumerate}[label=(\alph*)]
\item Show that $R = 436$
\item Find the tension in the tow bar.
The two vehicles come to a hill inclined at an angle $\alpha$ to the horizontal where $\sin \alpha = \frac { 1 } { 15 }$. The truck and the car move down a line of greatest slope of the hill with the tow bar parallel to the direction of motion. The truck's engine produces a constant driving force of magnitude 2100 N . The magnitudes of the resistances to motion on the truck and the car are 640 N and 436 N respectively.
\item Find the magnitude of the acceleration of the truck and the car as they move down the hill.\\
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\hfill \mbox{\textit{Edexcel M1 2018 Q7 [10]}}