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Question

A block of mass 1 kg lies on a hotrizontal surface in a truck. The coefficient of static friction between the block and the surface is 0.6. If the acceleration of the truck is $$5 m/sec^2$$, find out the frictional force acting on the block.


A
10N
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B
6N
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C
4N
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D
5N
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Solution

The correct option is D 5N
In these type of question we assume first there is no relative motion between surfaces and find out  friction co-efficient. If this friction co-efficient is less than static friction co-efficient then our assumption is right. Otherwise we solve using static friction Co-efficient.
Normal force due to truck on block (N) = mg = 1$$\times$$ 10 = 10 Newton
Block will move due to friction force 
Friction force = $$\mu N$$ = $$10\mu$$

Assuming no sliding between surfaces
Acceleration of block (a)= acceleration of truck = 5 $$m{ s }^{ -2 }$$
Writing force equation,
$$10\mu $$ = ma
$$10\mu $$ = 1$$\times$$5
$$\mu$$ = 0.5 which is less than 0.6(static friction co-efficient), so our assumption was correct. 

So friction force = $$\mu \times N$$
                         = 0.5 $$\times$$10 = 5 Newton

Physics

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