Posted by Litany on Friday, November 13, 2009 at 6:02am.
the answer is 400 N
first we find the normal force on the small cube:
F=ma (where f=force,a=acceleration,m=mass)
a=f/m
acceleration on small box is same as that on the large box. let force to find be P.
then:
a=p/(25kg+4kg)
a=p/(29kg)m/s^2
force acting on small box:
f=ma
f=4*(p/29)N(normal force)
friction force= Us*(normal force) Us is coeff. of static friction.
friction= 0.71*(4*p/29)
weight= mg= 4*9.8
for the object(small box) not to slide down the friction force b/w the two objects have to be exactly the same as the weight of the object.
0.71*(4*p/29)=4*9.8
solving..
p= 400.29N
Start by drawing the fbd of the little box. Friction up, gravity down, normal towards the right. From that we can tell friction is the same as gravity.
Fg:
Fg=m•g so Fg=4•9.8
Fg=39.2
Ff=Fg so Ff=39.2
Fn:
Ff=μ•Fn so 39.2=.71•Fn
Fn=55.21126761
Calculate the acceleration:
ΣF=M•A
ΣFx=Fn=m•a
ΣFx=55.21126761=4•a
55.21126761/4=a
a=13.0828169
Then draw the fbd for the big box. Fn going up, left, and right and Fg going down. Calculate the y axis forces and the Fn going to the left.
Fg:
Fg=m•g so Fg=25•9.8
Fg=245 and Fn does as well
Fn:
Fn=55.21 because we solved for that on the small box. Bc of Newton's 3rd law we know those are paired forces.
ΣF=m•a
ΣFx=Fn-55.12=25•13.08
Fn-55.12= 345.0704225
Fn=400.28
The answer is 400.28