How Is the Mass of Block B Calculated in a Friction-Affected Pulley System?

In summary, the problem involves two blocks connected over a pulley, with block A sliding down an incline at constant speed. The mass of block A is given as mA and the coefficient of kinetic friction between A and the incline is Uk. The angle of the incline is theta. Using the equation F=ma and considering acceleration to be 0, the mass of block B can be expressed as [m1gsin(theta) - m1gcos(theta)Uk] / g. This answer has been verified.
  • #1
martyk
4
0

Homework Statement



In figure 6-36, two blocks are connected over a pulley. The mass of block A is mA and the coeffcient of kinetic friction between A and the incline is Uk. Angle of the incline is theta. Block A slides down the incline at constant speed. What is the mass of block B? Express your answer in terms of the variables given.

http://img121.imageshack.us/img121/9748/fig636.gif

Homework Equations



F = ma

The Attempt at a Solution



Taking acceleration to be 0, because speed is constant. And that T1 = T2, i came to the answer of

[m1gsin(theta) - m1gcos(theta)Uk] / g = mass of the 2nd block

Can I get a verification
 
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  • #2
Yes, that is correct.
 
  • #3
on this answer?

Your solution looks correct. By setting the acceleration to 0, you are accounting for the effect of friction on the block's motion. Since the blocks are connected by a pulley, the tension in the string is equal on both sides, allowing you to equate the forces acting on each block. Your expression for the mass of block B takes into account the weight of block A, the normal force from the incline, and the frictional force. Well done!
 

FAQ: How Is the Mass of Block B Calculated in a Friction-Affected Pulley System?

What is Newton's first law with friction?

Newton's first law states that an object at rest will remain at rest, and an object in motion will continue in motion with a constant velocity, unless acted upon by an external force. With friction, this means that an object at rest will not move unless a force is applied to overcome the frictional force.

How does friction affect Newton's second law?

Newton's second law states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. With friction, the net force acting on an object will be reduced due to the frictional force, resulting in a smaller acceleration.

Can friction ever be helpful in following Newton's third law?

Newton's third law states that for every action, there is an equal and opposite reaction. In the case of friction, the action is the force applied to an object, and the reaction is the frictional force acting in the opposite direction. While friction may be seen as hindering motion, it is necessary for objects to stay in place and for us to have traction while walking or driving.

How does the coefficient of friction affect Newton's laws?

The coefficient of friction is a measure of the amount of friction between two surfaces. It affects Newton's laws by determining the strength of the frictional force. A higher coefficient of friction means a stronger frictional force, which will have a greater impact on the object's motion.

How does friction impact rolling objects and Newton's laws?

Friction affects rolling objects by creating a resistive force that slows down the object's motion. This means that rolling objects will not maintain a constant velocity, as stated in Newton's first law, and will require a force to keep them in motion, in accordance with Newton's second law. The coefficient of friction also plays a role in the strength of the resistive force on rolling objects.

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