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 0.82-kg air cart is attached to a spring and allowed to oscillate.

Part A

If the displacement of the air cart from equilibrium is x=(10.0cm)cos[(2.00s?1)t+?], find the maximum kinetic energy of the cart.

Express your answer using two significant figures.

Part B

Find the maximum force exerted on it by the spring.

Express your answer using two significant figures.

Added Mon, 06 Jul '15

Community

1

Add a Comment

Solutions

0

x = xmax*cos(omega*t + phi)

xmax is the amplitude

omega is the angular frequency

phi is the phase angle

For the mass-spring system, the theoretical omega is calculated as:

omega = sqrt(k/m)

We know omega and m, solve for k:

k = m*omega^2

And, since we know xmax and an expression for k, we can find the maximum strain potential energy, which is also equal, by energy conservation, to the maximum kinetic energy:

KEmax = SPEmax = 1/2*k*xmax^2

Thus:

KEmax = 1/2*m*omega^2*xmax^2

And, to find the maximum force exerted by the spring, just simply use Hooke's law. Forget about the negative sign, it isn't of interest to us. Yes, we do know it points opposite the displacement.

Fmax = k*xmax

Fmax = m*omega^2*xmax

Summary:

A) KEmax = 1/2*m*omega^2*xmax^2

B) Fmax = m*omega^2*xmax

A) KEmax = 0.5*0.82*4*0.1^2

= 0.0164J

b)Fmax = 0.82*4*0.1

= 0.328N

Added Mon, 06 Jul '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.