Moderate -0.3 This is a straightforward energy conservation problem requiring students to apply the work-energy principle with gravitational PE, KE, and work against resistance. It involves standard formula substitution (ΔKE + ΔPE + work against resistance = 0) with no conceptual tricks, making it slightly easier than average for M1.
2 An object of mass 8 kg slides down a line of greatest slope of an inclined plane. Its initial speed at the top of the plane is \(3 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) and its speed at the bottom of the plane is \(8 \mathrm {~m} \mathrm {~s} ^ { - 1 }\). The work done against the resistance to motion of the object is 120 J . Find the height of the top of the plane above the level of the bottom.
For using 'loss of PE = gain in KE + WD against resistance'
PE loss \(= \frac{1}{2}8(8^2 - 3^2) + 120 (= 340 \text{ J})\)
A1
\([340 = 8gh]\)
DM1
For using \(PE = mgh\)
Height is 4.25 m
A1
[4]
For attempting to eliminate \(a\), \(a\) and \(s\) from the equations \((80\sin\alpha - 120/s = 8a\) \(64 - 9 = 2as, h = s\sin\alpha)\)
M1
\(80s \sin - 120 = 4(64 - 9)\)
M1
\(\to 80h - 120 = 220\)
\(\to h = 4.25\)
A1
| M1 | For using 'loss of PE = gain in KE + WD against resistance'
PE loss $= \frac{1}{2}8(8^2 - 3^2) + 120 (= 340 \text{ J})$ | A1 |
$[340 = 8gh]$ | DM1 | For using $PE = mgh$
Height is 4.25 m | A1 | [4] | SR for candidates who assume without justification that the resistance to motion is constant, usually implicitly by using constant acceleration formulae (max 3/4) For using Newton's second law with 3 terms, $v^2 - u^2 = 2as$ and $h = s \sin\alpha$ | M1
For attempting to eliminate $a$, $a$ and $s$ from the equations $(80\sin\alpha - 120/s = 8a$ $64 - 9 = 2as, h = s\sin\alpha)$ | M1
$80s \sin - 120 = 4(64 - 9)$ | M1
$\to 80h - 120 = 220$ |
$\to h = 4.25$ | A1
2 An object of mass 8 kg slides down a line of greatest slope of an inclined plane. Its initial speed at the top of the plane is $3 \mathrm {~m} \mathrm {~s} ^ { - 1 }$ and its speed at the bottom of the plane is $8 \mathrm {~m} \mathrm {~s} ^ { - 1 }$. The work done against the resistance to motion of the object is 120 J . Find the height of the top of the plane above the level of the bottom.
\hfill \mbox{\textit{CAIE M1 2011 Q2 [4]}}