Algebraic expressiong for two blocks

[jenador]

Homework Statement

Two blocks are sliding to the right across a horizontal surface, as the drawing shows. In Case A the masses of both blocks are 2.2 kg. In Case B the mass of block 1, the block behind, is 7.0 kg, and the mass of block 2 is 3.5 kg. No frictional force acts on block 1 in either Case A or Case B. However, a kinetic frictional force does act on block 2 in both cases and opposes the motion. In the drawing, the direction to the right is the positive direction.

picture: http://www.webassign.net/CJ/p4-118alt.gif

What is the algebraic expression for the magnitude P of the forces vector P and -vector P with which the blocks push against each other? Express your answer in terms of the mass m1 of block 1, the mass m2 of block 2, and the magnitude fk of the kinetic frictional force that acts on block 2. The direction to the right in the drawing is the positive direction. (Answer using m_1 to be the mass of block 1, m_2 to be the mass of block 2, and f_k to be the kinetic frictional force fk.)

in other words, write out an expression using m_1, m_2, and friction of kinetic force, fk.

i do not understand how you can derive a force equation corresponding to opposing forces without including a variable for acceleration. since both blocks in each case will have f=ma, shouldn't the expression be something like f=(m_1)a+m_2*a? can someone please give me a hint on how to solve this? what am i missing

 

[PhanthomJay]

i do not understand how you can derive a force equation corresponding to opposing forces without including a variable for acceleration. since both blocks in each case will have f=ma, shouldn't the expression be something like f=(m_1)a+m_2*a? can someone please give me a hint on how to solve this? what am i missing

Yes, so what is the net force acting on the system of blocks? That will determine the acceleration. Then you can isolate the blocks in a free body diagram to solve for the contact force between the 2.

 

[nlightner]

?

The algebraic expression for the magnitude P of the forces vector P and -vector P with which the blocks push against each other can be written as:

P = m1a1 + m2a2 + fk

Where m1 and m2 are the masses of block 1 and block 2 respectively, a1 and a2 are their respective accelerations, and fk is the magnitude of the kinetic frictional force acting on block 2.

In this case, since there is no friction acting on block 1, its acceleration is equal to the acceleration of the system as a whole, which we can denote as a. So the expression can also be written as:

P = (m1 + m2)a + fk

This expression takes into account the fact that both blocks will have the same acceleration since they are connected and moving together. The kinetic frictional force acting on block 2 will act in the opposite direction and will be subtracted from the total force.

It is important to note that in this scenario, the acceleration of the blocks is not constant and will depend on the magnitude of the kinetic frictional force. Therefore, the expression for P will also vary depending on the specific values of the masses and the frictional force.