• Support PF! Buy your school textbooks, materials and every day products Here!

Find minimum force to move block

  • Thread starter the_sense
  • Start date
  • #1
2
0

Homework Statement


"Figure 1 shows two wedge blocks A and B, weighing 1000 N and 50 N, respectively, in contact. The coefficient of friction between all contacting surfaces is 0.1 . What would be the smallest value of P required to push the block A upwards? What would be its value if there were no friction?"

Ans, with friction: 887.3 N (given)
Ans, without friction: 577.4 N (given)
The gray rectangle in the picture is part of a separate problem.

Homework Equations



[itex]
ƩF = 0
[/itex]

[itex]
F_f = μF_N
[/itex]

The Attempt at a Solution


I have solved problems of this nature before. I have a good understanding of vector addition and statics. I solved the problem sans friction in the following manner:

[itex]
F_N = W_A /cos30
[/itex]

[itex]
ƩF_x = 0 ∴ F_N \cdot cos60 = P
[/itex]

[itex]
P = W_A \cdot cos60 /cos30 = 577.4 N
[/itex]

With friction, however, I run into a problem: The side walls in contact with A exert a frictional force downwards. This of course depends on the normal force exerted by those walls, which partly balance the horizontal components of the normal and frictional forces exerted by B on A. But as far as I can tell, the vertical component of the normal force is equal to the sum of the weight and these frictional forces. So I encounter what appears to be a catch-22. I have tried various methods employing systems of equations but I get nowhere.
 

Attachments

Last edited:

Answers and Replies

  • #2
Simon Bridge
Science Advisor
Homework Helper
17,847
1,644
I would try the work-energy relation and conservation of energy.
Otherwise you'd have to draw the free body diagrams.

The wrinkle I see is that block A also gets pressed against the side of the whatsits that constrains it to the vertical - in proportion to the applied force. (The applied force ends up creating a couple with the reaction forces in the constraint - I suspect that this is "overthinking" the problem at the level it is presented.)

You should get a number of equations where it appears that things have a circular dependence - and you can cancel terms.
 
  • #3
2
0
Ok, I will try that. Thanks for the help.
 
  • #4
Simon Bridge
Science Advisor
Homework Helper
17,847
1,644
At least you have nice angles:

sin(30)=1/2
cos(30)=(√3)/2
tan(30)=1/√3

... you can replace the trig functions with the fractions (keep the surd until the end).
Most of them seem to come out to 1/2.
In all your triangles for this problem, find the 30deg angle and do all your trig with that as theta
... you will get less confused.
 
  • #5
Simon Bridge
Science Advisor
Homework Helper
17,847
1,644
Conservation of energy means: ##E_{in} = E_{out} + E_{lost}##.

Applied force P over distance x, energy input: Ein = Px.

This energy goes to gravitational PE, ##U##, in A, and three lots of friction:
E1: between B and the ground
E2: between the blocks
E3: between A and the restraining channel.

So: ##E_{in}=U+E_1+E_2+E_3##

##U=w_A\Delta y:w_A=m_Ag=1000\text{N}##
B moving x means A moves up ##\Delta y=x\tan(30^\circ)=x/\sqrt{3}##
##\Rightarrow U=\frac{1}{\sqrt{3}}w_Ax##

Without friction: ##P=\frac{1}{\sqrt{3}}w_A##

... which is where you are up to ;)


As you have observed, the friction is the tricky bit.

The ith energy lost to friction is ##E_i=f_id## where d is the distance moved against friction and ##f_i=\mu N_i## ... so you are finding expressions for the "normal force", ##N_i## ... which will mean drawing free-body diagrams. Assuming flush surfaces will probably avoid having to think about couples.

i.e. For ##i=1## (the first friction): ##d=x##, and ##N_1 = w_B+\text{<contributions from }w_A\text{>} ##

Try to express each normal force in terms of P and x and constants, where applicable.
You'll end up with something like ##Px=\big(p(P)+q\big)x## where you can eliminate x and solve for P.
 

Related Threads on Find minimum force to move block

  • Last Post
Replies
0
Views
2K
  • Last Post
Replies
4
Views
15K
Replies
6
Views
326
Replies
20
Views
14K
  • Last Post
Replies
7
Views
3K
Replies
1
Views
1K
  • Last Post
Replies
2
Views
48K
Replies
5
Views
3K
Replies
6
Views
438
  • Last Post
Replies
5
Views
984
Top