About tension.......

[albertlee]

I find something contradictory to these two questions and there answers....

 

1) A breakdown truck tows a car of mass 1000kg along a level road, and accelerates 0.5m/s/s. What is the tension in the towline???

 

Ans: 1000/2 = 500N = the tension

 

2) A trailer of mass 1000kg is towed by means of a rope attached to a car moving at a steady speed along a level road. The tension in the rope is 400N, why is it not zero????

 

Any idea to the question in bold????

 

thx

 

Albert

[swansont]

By Newton's first law, since the velocity is constant, the net force must be zero. Since T is not zero, what does that tell you about the presence of other forces on the car, in the horizontal direction?

[coquina]

Out of my league here, but does it have anything to do with the fact that a rope will stretch (if it is nylon, it will stretch a lot) a twisted multiwire cable will stretch a minimal amount.

[J.C.MacSwell]

I find something contradictory to these two questions and there answers....

 

1) A breakdown truck tows a car of mass 1000kg along a level road' date=' and accelerates 0.5m/s/s. What is the tension in the towline???

 

Ans: 1000/2 = 500N = the tension

 

2) A trailer of mass 1000kg is towed by means of a rope attached to a car moving at a steady speed along a level road. The tension in the rope is 400N, [b']why is it not zero????[/b]

 

Any idea to the question in bold????

 

thx

 

Albert

 

Are you assuming no friction?

[swansont]

Out of my league here, but does it have anything to do with the fact that a rope will stretch (if it is nylon, it will stretch a lot) a twisted multiwire cable will stretch a minimal amount.

 

In the wonderful world of introductory physics problems, ropes are usually massless and don't stretch, unless that's the specific problem under scrutiny.

[YT2095]

the steady speed will only require a "top up" force to maintain it`s momentum, that force to "Top up" is required to overcome natural friction in bearings and drag etc...

 

when in acceleration you`re constantly applying NEW force to make it "go faster" even at a steady increase. so 100N of that force is used to accelerate and the 400n is used to overcome the friction.

 

that`s my reasoning anyway

[ans]

Maybe assuming there is friction, air resistance (ie there is an opposing force)

 

or perhaps is it something to do with the pull of the trailer on the car??

[Johnny5]

I find something contradictory to these two questions and there answers....

 

1) A breakdown truck tows a car of mass 1000kg along a level road' date=' and accelerates 0.5m/s/s. What is the tension in the towline???

 

Ans: 1000/2 = 500N = the tension

 

2) A trailer of mass 1000kg is towed by means of a rope attached to a car moving at a steady speed along a level road. The tension in the rope is 400N, [b']why is it not zero????[/b]

 

Any idea to the question in bold????

 

thx

 

Albert

 

Albert, consider things initially. You have a trailer sitting on the planet earth. The trailer has 1000 kilograms of inertia. Then there is a rope attached to it, and a car that is to pull the trailer.

 

Initially, there is no tension in the rope, its just hanging there. Then the car is turned on, and slowly moves fowards, until the rope is horizontal. At that moment in time, the tension in the rope is zero, and we have three objects at rest relative to each other...

 

1. trailer

2. rope

3. car

 

Now, as the car inches fowards, the rope stretches slightly (this fact comes from reality).

 

And while the rope is stretching, the center of mass of the trailer isn't changing position in the rest frame of the earth (much). The car pulls more and more, and the tension in the rope increases until finally the trailer starts moving in the rest frame of the earth.

 

There was a "frictional force" which the car had to overcome first, in order to get the trailer to accelerate in the rest frame of the earth.

 

In introductory physics, that force is proportional to the weight of the trailer. The weight of the trailer arises from the fact that the trailer is in a gravitational field. In introductory physics we have

 

W = weight = m g

 

m is the inertial mass of the trailer

g is the acceleration due to earths gravity at the surface of the earth, and local to the trailer. In SI units... g = 9.8 m/s^2, by experiment.

 

The magnitude of the force due to friction is given by:

 

[math] F_f = \mu_s N [/math]

 

Where N is the normal force, and "mu sub s" is the coefficient of static friction between the trailer and the earth. The normal force has the same magnitude as the weight of the trailer, but its direction is opposite to the trailer's weight. That is:

 

W+N=0

 

Hence, there is no motion of the trailer up into the air, or sinking into the earth.

 

The value of the coefficient of static friction depend upon the particular objects in question, and has to be measured.

 

Now, once that frictional force is overcome, the trailer and car are moving together (collectively) in unison, at the same speed.

 

If it is true that a frictional force acts upon the trailer at all moments in time whilst its moving along the road at a constant speed, the rope must always be applying an equal and opposite force to the trailer by Newton's third law. (where we assume Newton's third law is true in the frame of earth, in which the speed is constant.)

 

Therefore, the tension in the string cannot be zero, because it is exerting a force on the trailer equal to the frictional force of the road on the trailer, but in the opposite direction.

 

And it is true that a frictional force acts upon the trailer as it moves along the road.

 

Hence the tension in the string cannot be zero, even when the car isn't accelerating relative to the road at rest.

 

Regards