Standard +0.3 This is a straightforward work-energy problem requiring application of the work-energy principle with one force at an angle. Students must equate work done by pulling force minus work against resistance to change in kinetic energy, then solve for the angle using basic trigonometry. It's slightly easier than average as it's a standard textbook application with clear given values and a single unknown.
2 A box of mass 25 kg is pulled in a straight line along a horizontal floor. The box starts from rest at a point \(A\) and has a speed of \(3 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) when it reaches a point \(B\). The distance \(A B\) is 15 m . The pulling force has magnitude 220 N and acts at an angle of \(\alpha ^ { \circ }\) above the horizontal. The work done against the resistance to motion acting on the box, as the box moves from \(A\) to \(B\), is 3000 J . Find the value of \(\alpha\).
For using \(KE = \frac{1}{2}mv^2\) or \(WD = Fd\cos\alpha\)
Gain in \(KE = \frac{1}{2}(25)(3^2)\) or \(WD\) by pulling force \(= 220 \times 15\cos\alpha\)
A1
\(WD\) by pulling force \(= 220 \times 15\cos\alpha\) or Gain in \(KE = \frac{1}{2}(25)(3^2)\)
B1
\([3300\cos\alpha = 112.5 + 3000]\)
M1
For using \(WD\) by pulling force \(= KE\) gain \(+ WD\) against resistance
\(\alpha = 19.4\)
A1
5 marks total
## Question 2:
| Answer/Working | Mark | Guidance |
|---|---|---|
| (energy/work method) | M1 | For using $KE = \frac{1}{2}mv^2$ or $WD = Fd\cos\alpha$ |
| Gain in $KE = \frac{1}{2}(25)(3^2)$ or $WD$ by pulling force $= 220 \times 15\cos\alpha$ | A1 | |
| $WD$ by pulling force $= 220 \times 15\cos\alpha$ or Gain in $KE = \frac{1}{2}(25)(3^2)$ | B1 | |
| $[3300\cos\alpha = 112.5 + 3000]$ | M1 | For using $WD$ by pulling force $= KE$ gain $+ WD$ against resistance |
| $\alpha = 19.4$ | A1 | **5 marks total** |
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2 A box of mass 25 kg is pulled in a straight line along a horizontal floor. The box starts from rest at a point $A$ and has a speed of $3 \mathrm {~m} \mathrm {~s} ^ { - 1 }$ when it reaches a point $B$. The distance $A B$ is 15 m . The pulling force has magnitude 220 N and acts at an angle of $\alpha ^ { \circ }$ above the horizontal. The work done against the resistance to motion acting on the box, as the box moves from $A$ to $B$, is 3000 J . Find the value of $\alpha$.
\hfill \mbox{\textit{CAIE M1 2013 Q2 [5]}}