Calculating Velocity of 6000 lb Truck Around 650 ft Curve

[cowgiljl]

Truck weighs 6000 lbs The truck is going around a curve with a radius of 650 ft. The max friction force the road can exert is 1125 lbs.Its velocity needs to be calculated ft/sec.

Now I now F=ma and Ff = m*(v^2/r)
I also now that 1 pound = 4.448 N

problem is i have 3 different answers by trying it different ways

a) v = 62.6 ft/sec
b) v = 11.04 ft/sec
c) v = 58.88 ft/sec

Which one is the right one

This is the final problem I have to do before i have to turn in my physics notebook and take my final exam today at 9 am

any assistance would be great

thanks

 

[himanshu121]

B) is correct
i don't know how u reached the other results Pls show it

 

[harsh]

I think there is a mistake in dimension somewhere in there. Actually, the frictional force must be converted to Newtons and the weight of the truck must be converted to kg. Then, you can use [

f = ma
f = v^2 / r

(1125 lbs)*(4.448 N/lbs) = [(6000 lbs * 4.448 N/lbs)/9.81 m/s^2]*v^2/r

You will get around 34 ft/sec.

 

[himanshu121]

B is correct harsh u are given max frictional force why u are dividing by 9.81

 

[HallsofIvy]

Actually, the frictional force must be converted to Newtons and the weight of the truck must be converted to kg.

Why? You are given all the information in the "English" system and asked for the result in the "English" system. F= ma and F= mv²/r are true in any system. Why convert to metric?

 

[harsh]

Right, but then you don't really get the correct units.
Its like you are canceling pounds over pounds, so the left side of the equation is unitless.

 

[himanshu121]

The max friction force the road can exert is 1125 lbs

It should be 1125lbs m/s^2

 

[ShawnD]

Originally posted by cowgiljl
Truck weighs 6000 lbs The truck is going around a curve with a radius of 650 ft. The max friction force the road can exert is 1125 lbs.Its velocity needs to be calculated ft/sec.

Now I now F=ma and Ff = m*(v^2/r)
I also now that 1 pound = 4.448 N

problem is i have 3 different answers by trying it different ways

a) v = 62.6 ft/sec
b) v = 11.04 ft/sec
c) v = 58.88 ft/sec

Which one is the right one

I'm getting the first answer. I've never actually used the imperial system before; it's just weird.

$$F = \frac {mv^2}{r}$$

$$\frac {Fr}{m} = v^2$$

we have to find the mass of the thing. divide the weight by the acceleration to get the mass.

$$m = \frac {F}{a}$$

$$m = \frac {6000}{32.2}$$

$$m = 186.3$$ i think that's in slugs

now back to the other formula

$$v = \sqrt {\frac {Fr}{m}}$$

$$v = \sqrt {\frac {(1125)(650)}{186.3}}$$

$$v = 62.65$$