Two identical blocks are placed on two different horizontal surfaces, P and Q

PHYSICS · Multi-part · A Level · Physics · Mechanics and materials · Mechanics and materials

Problem

Two identical

4\,\text{kg}

blocks are placed on two different horizontal surfaces, P and Q. The coefficients of friction are: • Surface P:

\mu_s=0.45

\mu_k=0.40

• Surface Q:

\mu_s=0.30

\mu_k=0.20

A horizontal force

F

is applied on each block and increased uniformly from

0

40\,\text{N}

. Thereafter the force is kept fixed at

25\,\text{N}

while each block slides a further

6\,\text{m}

. (i) For each surface, write an expression for the frictional force

f

acting on the block as a function of the applied force

F

in the interval

0\le F\le40\,\text{N}

. (ii) On a common set of axes, draw the graphs of

f

versus

F

for the two surfaces for

0\le F\le40\,\text{N}

. Clearly indicate all characteristic values on both axes. (iii) Using the information from your graphs, calculate the work done against friction on each block while it slides the

6\,\text{m}

under the constant

25\,\text{N}

pull. (iv) Based on your results, state with justification which surface is preferable if one wishes to minimise energy loss while still achieving good resistance to initial slipping.

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