A Sled in the Wind

Reuel · 2011-02-21 03:45:47

"Newton's Second Law, F=m*a, may be viewed as W = m*g where W is the weight in pounds and g is gravity. A sled weighing 100 lbs is being pushed in a straight line against the wind by a force of 10 lbs. Friction is negligible but there is an air resistance whose magnitude in pounds is equal to twice the velocity of the sled in feet per second.

"If the sled starts from rest, find the velocity and the distance traveled at the end of one second."

These physics-type questions throw me off. I have never had physics. We know the sled weighs 100 pounds and it's being pushed by 10 pounds of force on the horizontal... and we know that the wind has a magnitude of twice the velocity of the sled.

How is a problem such as this started? Does one find a position function and then differentiate? What is the difference between mass and weight? How should this solution be started?

Thanks for the help.

Bob · 2011-02-21 05:04:38

hi Reuel,

so thats where your D.E. is going to come from.

Mass is the amount of stuff in an object (sorry that's not very technical) and is independant of where the object is; on the Earth, in space, on the Moon; the mass doesn't vary. It's measured in pounds etc or Kilograms in the metric system.

Weight is what we call the force exerted on a mass by gravity and is measured, just to be confusing, in pounds too.

See http://gwydir.demon.co.uk/jo/units/weight.htm#mass where an attempt is made to distinquish these.

In metric the unit of force is the Newton.

As weight depends on gravity, it'll be different on the Moon.

Orbiting the Earth you are weightless not because you have escaped the Earth's gravitational field or you wouldn't be orbiting! but because you are in free fall. That's another post in itself.

If you stand on some bathroom scales you really want to know your mass but people talk of 'weighing yourself' because the scales have a device in them to measure the force exerted by gravity; easy way to lose weight: jump out of a plane whilst standing on the scales; you're in free fall so you'll weigh nothing!

Got carried away there ... sorry; now back to the problem.

(i) Find the effective force (F) = 10 pounds-force accelerating you and 2V against acceleration.

(ii) Use F = ma to build the D.E. using a = dv/dt . ( m = 100 pounds-mass)

(iii) to get the distance travelled you'll need to integrate again using

's' is usually used for distance rather than 'd' because the D.E. would look odd with dd/dt.

Bob

Last edited by Bob (2011-02-21 05:09:58)

Reuel · 2011-03-09 03:47:34

Thanks, Bob. How does this look?

Let y be the distance the sled travels.

When y(0) = 0,

And so after 1 second in time, the sled as traveled 1.31 meters and with a velocity of 4.473 m/sec.

How does my math look?

Last edited by Reuel (2011-03-09 03:48:35)

Bob · 2011-03-09 07:51:12

hi Reuel,

Looks like you've got three posted questions.

I've got to do the washing up so I'll come back in a mo.

Sailboat question Ok ?

This post I'll check

Race cars. Looks like I'll have to think about this one so this will take a longer mo.

Back soon,

Bob

Bob · 2011-03-09 08:20:08

hi again,

Duties done so now for the problems.

Sled question

That looks exactly right.

My only problem is about pounds-weight and pounds-mass.

For years now, I've done all my problems in Newtons and kilograms so don't have any 'word' difficulties.

I see you've done 100/32 to get the mass using acceleration due to gravity as 32 ft /sec/sec. I guess that's ok.

The other mathematical bits are all fine.

Now I'll hop across to race cars.

Bob

Last edited by Bob (2011-03-09 08:20:43)

Math Is Fun Forum

#1 2011-02-21 03:45:47

A Sled in the Wind

#2 2011-02-21 05:04:38

Re: A Sled in the Wind

#3 2011-03-09 03:47:34

Re: A Sled in the Wind

#4 2011-03-09 07:51:12

Re: A Sled in the Wind

#5 2011-03-09 08:20:08

Re: A Sled in the Wind

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