ToughSTEM
Sign Up
Log In
ToughSTEM
A question answer community on a mission
to share Solutions for all STEM major Problems.
Cant find a problem on ToughSTEM?
0

Three blocks are connected on the table as shown below. The

coefficient of kinetic friction between the block of mass m2 and

the table is 0.310. The objects have masses of m1 = 4.75 kg, m2 =

1.10 kg, and m3 = 2.20 kg, and the pulleys are frictionless.

(a) Draw free-body diagrams for each of the objects.

(b) Determine the acceleration of each object, including its

direction.

m1: ___ m/s2 Direction?

m2: ___ m/s2 Direction?

m3: ___ m/s2 Direction?

(c) Determine the tensions in the two cords.

left cord ____ N

right cord ____ N

(d) If the tabletop were smooth, would the tensions increase,

decrease, or remain the same? Explain.

Edit
Added Sun, 03 Jul '16
Comment
Add a Comment
Solutions
0

let tension in left string is T1.

tension in right string is T2.

let acceleration of whole system is a m/s^2,towards left.

then for m1:

m1*g-T1=m1*a..(1)

for m2:

T1-T2-0.31*m2*g=m2*a..(2)

for m3:

T2-m3*g=m3*a..(3)

adding the three equations:

g*(m1-0.31*m2-m3)=a*(m1 m2 m3)

a=2.69 m/s^2

T1=33.77 N

T2=27.47 N

answers:

b)

m1: 2.69 m/s^2,downwards

m2: 2.69 m/s^2,leftward

m3: 2.69 m/s^2,,upwards

c) left cord=T1=33.77 N

right cord:T2=27.47 N

d)if table were smooth,the friction part will vanish.

then a=g*(m1-m2)/(m1 m2 m3)

=3.1 m/s^2

T2=m3*(g a)=28.38 N

T1=m1*(g-a)=31.8 N

so left cord tension will decrease while right cord tension will

increase.

Edit
Added Sun, 03 Jul '16
Comment
Add a Comment
Add Your Solution!
Close

Click here to
Choose An Image
or
Get image from URL
GO
Close
Back
Add Image
Close
What URL would you like to link?
GO
α
β
γ
δ
ϵ
ε
η
ϑ
λ
μ
π
ρ
σ
τ
φ
ψ
ω
Γ
Δ
Θ
Λ
Π
Σ
Φ
Ω
Copied to Clipboard

Add Your Solution
Sign Up
to interact with the community. (That's part of how we ensure only good content gets on ToughSTEM)
OR
OR
ToughSTEM is completely free, and its staying that way. Students pay way too much already.
Almost done!
Please check your email to finish creating your account!
Welcome to the Club!
Choose a new Display Name
Only letters, numbers, spaces, dashes, and underscores, are allowed. Can not be blank.
Great! You're all set, .
A question answer community on a mission
to share Solutions for all STEM major Problems.
Why
The Purpose
How
The Community
Give Feedback
Tell us suggestions, ideas, and any bugs you find. Help make ToughSTEM even better.