How Does Friction Affect the Acceleration and Tension in a Two-Block System?

[dkajsdk]

Homework Statement

A block of mass m = 0.500 kg rests on top of a block of mass M = 2.50 kg which is on the
floor. A string attached to the block of mass M is pulled so that its tension is T = 7.00 N
at a 25.0o angle to the horizontal as shown. The blocks move together across the
horizontal surface. The coefficient of static friction at the surface between the blocks is
μs = 0.410. There is no friction at the surface between block M and the floor.

a) What is the acceleration of the two-block system?

b) What is magnitude and direction of the total force (combination of normal force
and frictional force) on block m due to block M?

c) The tension T is now increased - what is the maximum tension, Tmax, with which
the string can be pulled such that the blocks continue to move together (i.e. that
the block of mass m does not start to slide on top of the block of mass M)?

Homework Equations

The Attempt at a Solution

I solved part a and got 2.11 m/s^2 but i have no clue about part b and c. please help me.

 

[PeroK]

For part b): what is happening to block m?

 

[dkajsdk]

For part b): what is happening to block m?

Since there is friction, block m is not moving. Only M is moving.?

 

[PeroK]

When the question says "the blocks move together ...", how do you interpret that?

 

[dkajsdk]

When the question says "the blocks move together ...", how do you interpret that?

An analysis that comes to mind is pulling a sled with a child on it...except there is no incline

 

[PeroK]

Is block m accelerating?

 

[dkajsdk]

Is block m accelerating?

no

 

[PeroK]

no

You might want to revise your answer to part a), where I imagine you calculated the acceleration of the two block system. You should recalculate for acceleration of mass M only?

How did you get 2.11m/s/s if block m doesn't move?

 

[dkajsdk]

You might want to revise your answer to part a), where I imagine you calculated the acceleration of the two block system. You should recalculate for acceleration of mass M only?

How did you get 2.11m/s/s if block m doesn't move?

I found the x and y components of the tension with the angle. Since acceleration is horizontal and not vertical, only the x component is considered. I used Newton's 2nd Law, 7cos25=ma, and when I solved for a, I got 2.11m/s^2. This is only for mass M (the one without friction). Was I supposed to include both blocks? If mass m is not moving, then shouldn't it be fine that we only consider block M?

 

[PeroK]

You might want to revise your answer to part a), where I imagine you calculated the acceleration of the two block system. You should recalculate for acceleration of mass M only?

How did you get 2.11m/s/s if block m doesn't move?

I reckon cos25 is about 0.9, so the horizontal force is about 6.3N.

That would accelerate block M - mass 2.5kg - at about 2.6 m/s/s.

Or, it would accelerate the system of block M and m - combined mass 3kg - at about 2.1m/s/s.

So, how did you get 2.1m/s/s assuming only block M moves?