Standard +0.3 This is a straightforward application of conservation of energy with standard M1 content. Students need to equate initial KE to gravitational PE gained, using sin α from tan α (a routine trigonometric step). It's a single-method, direct calculation with no problem-solving insight required, making it slightly easier than average.
1 A particle of mass 1.6 kg is projected with a speed of \(20 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) up a line of greatest slope of a smooth plane inclined at \(\alpha\) to the horizontal, where \(\tan \alpha = \frac { 3 } { 4 }\).
Use an energy method to find the distance the particle moves up the plane before coming to instantaneous rest.
\(\pm 1.6g \times x \times \frac{3}{5}\) \([=9.6x]\) or \(\pm\frac{1}{2}\times 1.6\times 20^2\) \([=320]\)
B1
For either the correct potential energy or kinetic energy term. Need not be evaluated.
\(\frac{1}{2}\times 1.6\times 20^2 = 1.6g\times x\sin\alpha\) where \(\sin\alpha = \frac{3}{5}\)
M1
Attempt at energy equation; 2 relevant terms. Dimensionally correct but allow sign errors. Allow sin/cos mix and \(\sin(36.869...)\) but \(\sin\alpha\) (oe) must have been substituted. M0 for \(1.6g\times x\times\frac{3}{4}\).
\(x = \frac{100}{3}\)
A1
Allow 33.3.
3
## Question 1:
| Answer | Marks | Guidance |
|--------|-------|----------|
| $\pm 1.6g \times x \times \frac{3}{5}$ $[=9.6x]$ or $\pm\frac{1}{2}\times 1.6\times 20^2$ $[=320]$ | **B1** | For either the correct potential energy or kinetic energy term. Need not be evaluated. |
| $\frac{1}{2}\times 1.6\times 20^2 = 1.6g\times x\sin\alpha$ where $\sin\alpha = \frac{3}{5}$ | **M1** | Attempt at energy equation; 2 relevant terms. Dimensionally correct but allow sign errors. Allow sin/cos mix and $\sin(36.869...)$ but $\sin\alpha$ (oe) must have been substituted. M0 for $1.6g\times x\times\frac{3}{4}$. |
| $x = \frac{100}{3}$ | **A1** | Allow 33.3. |
| | **3** | |
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1 A particle of mass 1.6 kg is projected with a speed of $20 \mathrm {~m} \mathrm {~s} ^ { - 1 }$ up a line of greatest slope of a smooth plane inclined at $\alpha$ to the horizontal, where $\tan \alpha = \frac { 3 } { 4 }$.
Use an energy method to find the distance the particle moves up the plane before coming to instantaneous rest.\\
\hfill \mbox{\textit{CAIE M1 2023 Q1 [3]}}