Moderate -0.8 This is a straightforward application of the work-energy theorem requiring only basic kinematics (finding displacement from constant acceleration) and the work-energy principle. The question guides students by explicitly stating 'by considering energy,' making it easier than average with no conceptual challenges beyond standard M1 content.
4 A load of mass 160 kg is lifted vertically by a crane, with constant acceleration. The load starts from rest at the point \(O\). After 7 s , it passes through the point \(A\) with speed \(0.5 \mathrm {~ms} ^ { - 1 }\). By considering energy, find the work done by the crane in moving the load from \(O\) to \(A\).
For finding the acceleration and using Newton's second law (3 terms) to find the tension in the rope, then multiplying by the distance
Work done is \(2820\) J
A1
# Question 4:
$[s = (0 + 0.5)/2 \times 7]$ | M1 | For using $(u+v)/2 = s/t$
$s = 1.75$ m | A1 | May be implied
PE gain $= 160g \times 1.75$ | B1ft |
KE gain $= \frac{1}{2} \times 160 \times 0.5^2$ | B1 |
$[WD = 2800 + 20]$ | M1 | For using $WD =$ PE gain $+$ KE gain
Work done is $2820$ J | A1 | [6]
**SR (max 4/6) for candidates who use a non-energy method:**
$[s = (0 + 0.5)/2 \times 7]$ | M1 | For using $(u+v)/2 = s/t$
$s = 1.75$ m | A1 |
$[a = 1/14,\ T = 160g + 160/14,\ WD = 1611.4... \times 1.75]$ | M1 | For finding the acceleration and using Newton's second law (3 terms) to find the tension in the rope, then multiplying by the distance
Work done is $2820$ J | A1 |
---
4 A load of mass 160 kg is lifted vertically by a crane, with constant acceleration. The load starts from rest at the point $O$. After 7 s , it passes through the point $A$ with speed $0.5 \mathrm {~ms} ^ { - 1 }$. By considering energy, find the work done by the crane in moving the load from $O$ to $A$.
\hfill \mbox{\textit{CAIE M1 2008 Q4 [6]}}