A particle, under the action of two constant forces, is moving across a perfectly smooth horizontal surface at a constant speed of 10 ms$^{-1}$ - AQA - A-Level Maths: Mechanics - Question 12 - 2019 - Paper 2
Question 12
A particle, under the action of two constant forces, is moving across a perfectly smooth horizontal surface at a constant speed of 10 ms$^{-1}$.
The first force act... show full transcript
Worked Solution & Example Answer:A particle, under the action of two constant forces, is moving across a perfectly smooth horizontal surface at a constant speed of 10 ms$^{-1}$ - AQA - A-Level Maths: Mechanics - Question 12 - 2019 - Paper 2
Step 1
Find the force balance for constant speed
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Answer
Since the particle is moving at a constant speed, the net force acting on it must be zero. Therefore, the equation for the forces can be set up as:
extFextnet​=extF1​+extF2​=0
Given:
\text{F}_1 = (400 ext{ i} + 180 ext{ j}) ext{ N}
\text{F}_2 = ( ext{p} - 180 ext{ j}) ext{ N}
This leads to:
(400exti+180extj)+(extp−180extj)=0
Step 2
Separate the components
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Answer
By separating the components, we get two equations:
For the i component:
400=0 (No exti direction force implies this is balanced)
For the j component:
180+(extp−180)=0
This simplifies to:
extp=0
Step 3
Circle the correct answer
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Answer
The only allowable value of extp that satisfies this equation is extp=400.
