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 $5m/se{c}^2$, find out the frictional force acting on the block.

• A. 10N
• B. 6N
• C. 4N
• D. 5N

Answer 1

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