Graphs-1(Physics)

Classical Mechanics Level 2

A block is placed on a rough horizontal plane. A time-dependent horizontal force F = k t F=kt acts the block, where t t is time and k k is a positive constant. Which of the following represents the acceleration-time graph of the block?

Details

  • The block has a coefficient of static friction μ s \mu_s with the surface, and a smaller coefficient of kinetic friction μ k \mu_k . Also Try my Easy Mechanics Set Easy Mechanics
a b c d

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Kandarp Singh by Kandarp Singh , 22, India

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3 solutions

Satvik Pandey
Aug 15, 2014

The force is directly proportional to time but it is placed on rough surface so there must be some frictional force acting on it. The block will not move if the applied force is less than that of the limiting value of frictional force.But as the applied force becomes equal to the limiting value of frictional force then the block suddenly comes in motion.So acceleration suddenly increases. Hence graph c is correct.

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At limiting case, F = 0 F = 0 Then as F F increases, a a increases from 0.

Kishore S. Shenoy - 5 years, 9 months ago

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The question should've mentioned μ s \mu_s and μ k \mu_k differently. It's there now!

Kishore S. Shenoy - 5 years, 9 months ago

How is slope of a-t graph linear if there is a kinetic coefficient of friction in option c?

Sandhya Saravanan - 5 years, 7 months ago
Kshitij Johary
Jul 22, 2014

From the formula itself, it is clear that the force is directly proportional to time. There will be a linear relationship shown by a straight line. Also, at a positive value of t, the body will have some acceleration which is not zero as shown in (d). Hence, option (c) is the right option.

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Deepanshu Gandhi
Oct 22, 2014

Here a time dependent force is acting on block. As the block is at rest initially it is facing static friction. A force more than static friction is required to make the block move. So initially block will remain at rest until force greater than frictional force is applied. After the applied force is greater than frictional force it will start moving uniform acceleration

1 Helpful 1 Interesting 1 Brilliant 1 Confused

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