A car of mass 1000 kg is towing a caravan of mass 750 kg along a straight horizontal road - Edexcel - A-Level Maths Mechanics - Question 2 - 2012 - Paper 1
Question 2
A car of mass 1000 kg is towing a caravan of mass 750 kg along a straight horizontal road. The caravan is connected to the car by a tow-bar which is parallel to the ... show full transcript
Worked Solution & Example Answer:A car of mass 1000 kg is towing a caravan of mass 750 kg along a straight horizontal road - Edexcel - A-Level Maths Mechanics - Question 2 - 2012 - Paper 1
Step 1
show that R=860
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Answer
To find R, we consider the entire system (car and caravan) as one unit. The total driving force is given as 3200 N. The total resistance force acting on the system includes the resistance of the caravan (R) and the resistance of the car (800 N).
Using Newton's second law, we can express the total force as:
Fnet=mtotalimesa
where:
mtotal=1000extkg+750extkg=1750extkg
a=0.88extm/s2
Thus, we have:
Fnet=1750imes0.88=1540extN
Next, set up the equation based on the forces:
3200−R−800=1540
Solving this gives:
R=3200−800−1540=860extN
Step 2
find the tension in the tow-bar
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Answer
To find the tension (T) in the tow-bar, we will analyze the forces acting specifically on the caravan. The net force acting on the caravan can be expressed as:
R−T=mcaravanimesa
where:
mcaravan=750extkg
a=0.88extm/s2
Substituting the values gives:
860−T=750imes0.88
Calculating the right side yields:
750imes0.88=660extN
So the equation becomes:
860−T=660
Rearranging gives:
T=860−660=200extN
