A question answer community on a mission

to share Solutions for all STEM major Problems.

to share Solutions for all STEM major Problems.

Cant find a problem on ToughSTEM?

0

A 32.3kg block (m1) is on a horizontal surface, connected to a 6.50kg block (m2) by a massless string as shown in the Figure below. The frictionless pulley has a radius R = 0.097m and a moment of inertia I=0.060 kg*m2. A force F = 237.7N acts on m1 at an angle theta = 32.7. There is no friction between m1 and the surface.

What is the upward acceleration of m2?

Added Sun, 21 Jun '15

Community

1

Add a Comment

Solutions

0

Look at how the forces break down. For block 1

SFx = m1*a = F*cos(q) - T1

where SFx is the sum of the forces in the x-direction, a is the acceleration, and T1 is the tension from the string. For block 2

SFy = m2*a = T2 - m2*g

where SFy is the sum of the forces in the y-direction, a is the acceleration, and T2 is the tension from the string. Considering the pulley now

St = I*a/r = r*T1 - r*T2

where St is the sum of the torque, I is the moment of inertia of the pulley, r is the radius of the pulley. Combining these three equations will let you solve for the acceleration.

I*a/r^2 = T1 - T2

T1 = F*cos(q) - m1*a

T2 = m2*a + m2*g

so we have

I*a/r^2 = F*cos(q) - m1*a - m2*a - m2*g

which rearranges to

(m1 + m2 + I/r^2)*a = F*cos(q) - m2*g

Solving for a yields

a = (F*cos(q) - m2*g)/(m1 + m2 + I/r^2)

a = (237.7*cos(32.7) - 6.5*9.8) / (6.5+32.3+(0.060/0.097^2))

a = 136.32711 / 45.1768

a = 3.0176

Added Sun, 21 Jun '15

Community

1

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

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.

to share Solutions for all STEM major Problems.

Why

The Purpose

The Purpose

How

The Community

The Community

Give Feedback

Tell us suggestions, ideas, and any bugs you find. Help make ToughSTEM even better.