Which Statements About Moving a Block Are True?

[sonutulsiani]

Homework Statement

A block of mass m is resting on a horizontal surface whose coefficient of static friction is μs.

http://bcs.whfreeman.com/WebPub/Physics/tiplerphysics6e_bridge/question_bank_images/fig5-65.png?2439

Which of the following statements (if any) are true?

A. If you want to apply the minimum possible force to move the block, you should apply it with the force pulling upward at an angle θmin = arctan μs.
B. The minimum force necessary to start the block moving is μs mg/ √1 + μs2.
C. Once the block starts moving, if you want to apply the least possible force to keep it moving, you should keep the angle at which you are pulling the same.

There may be more than 1 answer

Homework Equations

Fs=μs Fn

The Attempt at a Solution

No idea.

 

[tiny-tim]

Hi sonutulsiani!

Call the normal force N, and the friction force H.

Then do a vector triangle or x and y component equations for a fixed angle θ …

what do you get? ​

 

[tomcue]

I can provide an explanation and clarification of the concept of coefficient of static friction and how it relates to the given statements.

Coefficient of static friction (μs) is a measure of the amount of friction between two surfaces in contact when there is no relative motion between them. It is a dimensionless quantity and its value depends on the nature of the surfaces in contact.

Statement A is not entirely accurate. The minimum force required to move the block is not dependent on the angle at which the force is applied, but rather on the coefficient of static friction and the normal force (Fn) acting on the block. The correct equation for the minimum force required to move the block is Fmin = μs Fn.

Statement B is also not entirely accurate. The correct equation for the minimum force required to start the block moving is Fmin = μs mg, where m is the mass of the block and g is the acceleration due to gravity.

Statement C is correct. Once the block starts moving, the force required to keep it moving is less than the minimum force required to start it moving. This force (F) is given by the equation F = μk Fn, where μk is the coefficient of kinetic friction, which is usually lower than the coefficient of static friction. The angle at which the force is applied does not affect the force required to keep the block moving.

In conclusion, the correct statements are: B and C.