ToughSTEM
ToughSTEM
A question answer community on a mission
to share Solutions for all STEM major Problems.
Cant find a problem on ToughSTEM?
0
A 10.0-kg box resting on a horizontal, frictionless surface is attached to a 6.00-kg weight by a thin, light wire that passes over a frictionless pulley. The pulley has the shape of a uniform solid disk of mass 4.00kg and diameter 0.200m.

a) Find the acceleration of the box after the system is released.

b) Find the tension in the wire on both sides of the pulley.

c) Find the horizntal and vertical components of the force that axle exerts on the pulley.
Edit
Community
1
Comment
Solutions
0
mass of pulley ( solid disk) =4.00kg

radius= diameter/2 = 0.20 / 2 =0.1 m

moment of inertia=(1/2mr^2) = 0.5*4*(0.1)^2=0.02 kgm^2

mass of box = M = 10 kg

acceleration of box= a

net force on box=ma

but net force on box =tension in horizontal portion of wire =Th

Th= 10 a..........................(1)

tension in vertical portion of wire = Tv

weight suspended =mg=6*9.8 =58.8 N

net force on suspended weight = 58.8 - Tv

but net force on suspended weight =ma=6a

58.8 - Tv=6a

Tv=58.8 -6a .........................(2)

If alpha is angular acceleration of pulley,

Net torque=[ Tv -Th]*r=[Tv-Th ]0.1

Net torque=[58.8 - 6a- 10 a ]0.1

Net torque=[58.8-16a]0.1

but net torque= I alpha= Ia /r=0.02 a/0.1=0.2 a

0.2a=[58.8-16a]0.1--------(3)

a=3.2667 m/s^2

Th=10a=32.667 N

horizontal tension is 32.667 N

B) vertical tension=Tv=58.8-6a=39.1998 N

vertical tension is 39.1998 N

A) acceleration of box is 3.2667m/s^2

C) magnitude of the horizontal component of the force F that the axle exerts on the pulley=Th =32.667 N

magnitude of the vertical components of the force that the axle exerts on the pulley= Tv + weight of wheel= 39.1998+ 39.2=78.3998? N
Edit
Community
1
Comment
Close

Choose An Image
or
Get image from URL
GO
Close
Back
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

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!