Moderate -0.8 This is a straightforward energy conservation problem requiring only two steps: calculate initial GPE (mgh = 1.6×10×9 = 144J), calculate final KE (½mv² = ½×1.6×144 = 115.2J), then subtract to find work done against resistance (28.8J). It's simpler than average A-level questions as it involves direct application of standard energy formulas with no problem-solving insight required.
1 A particle of mass 1.6 kg is dropped from a height of 9 m above horizontal ground. The speed of the particle at the instant before hitting the ground is \(12 \mathrm {~ms} ^ { - 1 }\).
Find the work done against air resistance.
Use Newton's second law with 3 terms, allow sign errors. Allow *their* \(a \neq g\). Allow \(a\) if it isn't subsequently replaced with \(g\)
\(\text{WD} [= 3.2 \times 9] = 28.8\) J
A1
Alternative method for Question 1:
Answer
Marks
Guidance
Answer
Marks
Guidance
\((\text{KE} =) \frac{1}{2} \times 1.6 \times 12^2\) OR \(115.2\)
B1
Allow for the expression for KE
\((\text{Loss of PE} =) \pm 1.6g \times 9\) OR \(\pm 144\)
B1
Allow for the expression for PE
\(\text{WD} = 28.8\) J
B1
Allow if get \(-28.8\) and then say \(28.8\) without explanation. Do not allow \(-28.8\) as final answer to working, so if get \(28.8\) and state \(-28.8\) then ISW
3
## Question 1:
| Answer | Marks | Guidance |
|--------|-------|----------|
| $12^2 = 2 \times 9 \times a$, **OR** $a = 8$ | **M1** | Use of suvat to get an equation in $a$ |
| $1.6g - R = 1.6a$, [may see $R = 3.2$] | **M1** | Use Newton's second law with 3 terms, allow sign errors. Allow *their* $a \neq g$. Allow $a$ if it isn't subsequently replaced with $g$ |
| $\text{WD} [= 3.2 \times 9] = 28.8$ J | **A1** | |
**Alternative method for Question 1:**
| Answer | Marks | Guidance |
|--------|-------|----------|
| $(\text{KE} =) \frac{1}{2} \times 1.6 \times 12^2$ **OR** $115.2$ | **B1** | Allow for the expression for KE |
| $(\text{Loss of PE} =) \pm 1.6g \times 9$ **OR** $\pm 144$ | **B1** | Allow for the expression for PE |
| $\text{WD} = 28.8$ J | **B1** | Allow if get $-28.8$ and then say $28.8$ without explanation. Do not allow $-28.8$ as final answer to working, so if get $28.8$ and state $-28.8$ then ISW |
| | **3** | |
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1 A particle of mass 1.6 kg is dropped from a height of 9 m above horizontal ground. The speed of the particle at the instant before hitting the ground is $12 \mathrm {~ms} ^ { - 1 }$.
Find the work done against air resistance.\\
\hfill \mbox{\textit{CAIE M1 2023 Q1 [3]}}