| Exam Board | Edexcel |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2023 |
| Session | October |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Momentum and Collisions |
| Type | Pile-driver or hammer impact |
| Difficulty | Moderate -0.8 This is a straightforward M1 momentum question with three standard parts: (a) perfectly inelastic collision using conservation of momentum, (b) impulse calculation from momentum change, (c) work-energy or SUVAT with forces. All parts follow textbook methods with simple arithmetic and no problem-solving insight required. Easier than average A-level due to being purely procedural. |
| Spec | 6.02i Conservation of energy: mechanical energy principle6.03b Conservation of momentum: 1D two particles6.03f Impulse-momentum: relation |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| \(10 \times 1.8 = (0.2 + 1.8)v\) | M1 | Forms CLM equation, condone sign errors and extra \(g\)'s |
| \(v = 9\) (positive) | A1 | cao |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| For tent peg: \(I = \pm 0.2(v - 0)\) or For hammer: \(-I = \pm 1.8(v-10)\) | M1 A1 | Impulse-momentum equation, dimensionally correct, correct no. of terms. M0 if \(g\) included. A1 correct unsimplified equation |
| \(1.8\) Ns OR \(1.8\) kgms\(^{-1}\) | A1 | cao, must include units |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| \(0 = 9^2 + 2a(0.12)\) OR \(0 = 9^2 - 2a(0.12)\) | M1 A1 | Equation formed to find acceleration. Must be dimensionally correct with correct no. of terms. Note \(a = -337.5\) |
| \(2g - R = 2a\) OR \(R - 2g = 2a\) | M1 A1 | Use of \(F=ma\). A1: correct equation, \(a\) does not need substituting but must be consistent with first equation |
| \(R = 690\) or \(695\) | A1 | cao |
## Question 3(a):
| Answer/Working | Mark | Guidance |
|---|---|---|
| $10 \times 1.8 = (0.2 + 1.8)v$ | M1 | Forms CLM equation, condone sign errors and extra $g$'s |
| $v = 9$ (positive) | A1 | cao |
## Question 3(b):
| Answer/Working | Mark | Guidance |
|---|---|---|
| For tent peg: $I = \pm 0.2(v - 0)$ or For hammer: $-I = \pm 1.8(v-10)$ | M1 A1 | Impulse-momentum equation, dimensionally correct, correct no. of terms. M0 if $g$ included. A1 correct unsimplified equation |
| $1.8$ Ns **OR** $1.8$ kgms$^{-1}$ | A1 | cao, must include units |
## Question 3(c):
| Answer/Working | Mark | Guidance |
|---|---|---|
| $0 = 9^2 + 2a(0.12)$ **OR** $0 = 9^2 - 2a(0.12)$ | M1 A1 | Equation formed to find acceleration. Must be dimensionally correct with correct no. of terms. Note $a = -337.5$ |
| $2g - R = 2a$ **OR** $R - 2g = 2a$ | M1 A1 | Use of $F=ma$. A1: correct equation, $a$ does not need substituting but must be consistent with first equation |
| $R = 690$ or $695$ | A1 | cao |
**ALT 1:** $0.12 = \frac{(9+0)}{2}t$ then $(R-2g)t = 2\times 9$ → M1A1, M1A1, A1
**ALT 2:** $0.12R = \frac{1}{2}\times 2\times 9^2 + 2g\times 0.12$ → M2A2, A1
**N.B.** Using $u=10$ for 9: max M0A0M1A1A0. Using $s=12$: max M1A0M1A1A0.
---\begin{enumerate}
\item A hammer is used to hit a tent peg into soft ground.
\end{enumerate}
The hammer has mass 1.8 kg and the tent peg has mass 0.2 kg .\\
The hammer and tent peg are both modelled as particles and the impact is modelled as a direct collision.
Immediately before the impact, the tent peg is stationary and the hammer is moving vertically downwards with speed $10 \mathrm {~m} \mathrm {~s} ^ { - 1 }$
Immediately after the impact, the hammer and tent peg move together, vertically downwards, with the same speed $v \mathrm {~ms} ^ { - 1 }$\\
(a) Find the value of $v$\\
(b) Find the magnitude of the impulse exerted on the tent peg by the hammer, stating the units of your answer.
The ground exerts a constant vertical resistive force of magnitude $R$ newtons, bringing the hammer and tent peg to rest after they travel a distance of 12 cm .\\
(c) Find the value of $R$.
\hfill \mbox{\textit{Edexcel M1 2023 Q3 [10]}}