# Finding Velocity

## Homework Statement

The soap-box car has a weight of 110 lb, including the passenger but excluding its four wheels. Each wheel has a weight of 5 lb, radius of .5 ft, and a radius of gyration k = .3 ft, computed about an axis passing through the wheels axle. Determine the cars speed after it has traveled 100 ft starting from rest. the wheels roll without slipping. Neglect Air.

## Homework Equations

T1 = $$\sum$$U1-2 = T2

## The Attempt at a Solution

T1 = 0 because it starts from rest
for T2 the mass would be 110lb car pluss the 4 5lb wheels, converted to slugs of course, and the v is what i am looking for

im not sure about the middle term

I = mk3 = .1554*.32 = .013986

What else do i need

LowlyPion
Homework Helper
What force is acting on the soapbox?

Incline? Angle?

Fy = 130 lb

LowlyPion
Homework Helper
Fy = 130 lb

Isn't that just the weight?

T2 = .5mv2 + .5Iw2

=.5(130/32.2)v2 + .5(130/32.2).32w2

T2 = 325 / 161 v2 + 117 / 644 w2

v = .5w2

T2 = 221/322 w2

$$\sum$$U1-2 = V1 - V2, V = Wy

V1 = Wy = W(100sin30)

V2= 0

Therefore

100Wcos30 = 221 / 322 w2

Something aint right

LowlyPion
Homework Helper
Something aint right

First they have given you the weights. You need the mass.

Second what is sin30? Is that the angle I previously inquired about being given?

oops sorry, i didnt understand when u asked the incline angle

it is 30 degrees

and they hypotenus is 100ft, so 100sin30 = y = 50

&

I did convert to mass when i divided the weight 130 by 32.2

Also...

When do use the info on the wheels, r = .5, k = .3, w = 5 lb

LowlyPion
Homework Helper
oops sorry, i didnt understand when u asked the incline angle

it is 30 degrees

and they hypotenus is 100ft, so 100sin30 = y = 50

&

I did convert to mass when i divided the weight 130 by 32.2

Also...

When do use the info on the wheels, r = .5, k = .3, w = 5 lb

Oh, I see. You got it. I see the 32.2 now.

OK the radius of gyration basically gives you the I = m*Rg2

But for your linear translational kinetic energy you have a r = .5 ft

I = mk2 = (5/32.2).32 = 9/644 <-- Should i multiply this my 4 since there are 4 wheels

50W = 1/2(130/32.2)v2 + 1/2 (9/644)w2

w = v/.5

50W = (325/161)v2 + (9/1288)(v/.5)2

50W = 325/161 v2 + 9/322 v2

50w = 659 / 322 v2

v = (16100W) / 659 or v = 24.43095599W

Is this right so far, How do i find W

I = mk2 = (5/32.2).32 = 9/644 <-- Should i multiply this my 4 since there are 4 wheels

50W = 1/2(130/32.2)v2 + 1/2 (9/644)w2

w = v/.5

50W = (325/161)v2 + (9/1288)(v/.5)2

50W = 325/161 v2 + 9/322 v2

50w = 659 / 322 v2

v = (16100W) / 659 or v = 24.43095599W

Is this right so far, How do i find W

brain fart

W = 130 right

so v = 56.35622 ft/s

anyone agree, disagree

LowlyPion
Homework Helper
anyone agree, disagree

m*g*h = 50*130 = 6500 = 1/2*m*V2 + 1/2*I*ω2

I = 4*5/32.2*(.3)2 = .056

ω = V/.5

6500 = 1/2*(4.037 + .056)*V2

V = 56.36

Looks OK.