M1 Friction Question

There is a truck, at which a man pulls with a light inextensible rope at an angle θ to the horizontal. The man walks parallel to the track on which the truck is going to move.

Initially the magnitude of the tension in the rope is 100 N and θ=10 degrees. This tension is not sufficient to move the truck from rest.
So the man pulls harder to move the truck. The truck moves from rest against a constant resistance to motion of (100+44sin10) N. There is constant tension in the rope, θ=10 still. It takes the man 15 seconds to reach his normal walking speed of 1.5 ms^-1.

By resolving I can easily find that T=(m*a+F_R(max))/cosθ, where F_R(max) is the maximum resistive force and is equal to 100+44sin10. But I can't equate this to F_R(max)=mu*m*g because I have no mu, and without that, m appears to be unknown in the T expression. So when it asks:

With what force must the man pull on the rope to reach the speed of 1.5 ms^-1?

How can I do this without the value of m?

Original post by Big-Daddy

There is a truck, at which a man pulls with a light inextensible rope at an angle θ to the horizontal. The man walks parallel to the track on which the truck is going to move.

Initially the magnitude of the tension in the rope is 100 N and θ=10 degrees. This tension is not sufficient to move the truck from rest.
So the man pulls harder to move the truck. The truck moves from rest against a constant resistance to motion of (100+44sin10) N. There is constant tension in the rope, θ=10 still. It takes the man 15 seconds to reach his normal walking speed of 1.5 ms^-1.

By resolving I can easily find that T=(m*a+F_R(max))/cosθ, where F_R(max) is the maximum resistive force and is equal to 100+44sin10. But I can't equate this to F_R(max)=mu*m*g because I have no mu, and without that, m appears to be unknown in the T expression. So when it asks:

With what force must the man pull on the rope to reach the speed of 1.5 ms^-1?

How can I do this without the value of m?

Where did you get this question from? I haven't tried it but it looks like there is insufficient information. Have you put the question in your own words?

Edit: I've looked at it and we have 3 equations and 4 unknowns.

(edited 11 years ago)

Reply 2

Brister

7

Original post by Big-Daddy

There is a truck, at which a man pulls with a light inextensible rope at an angle θ to the horizontal. The man walks parallel to the track on which the truck is going to move.

Initially the magnitude of the tension in the rope is 100 N and θ=10 degrees. This tension is not sufficient to move the truck from rest.
So the man pulls harder to move the truck. The truck moves from rest against a constant resistance to motion of (100+44sin10) N. There is constant tension in the rope, θ=10 still. It takes the man 15 seconds to reach his normal walking speed of 1.5 ms^-1.

By resolving I can easily find that T=(m*a+F_R(max))/cosθ, where F_R(max) is the maximum resistive force and is equal to 100+44sin10. But I can't equate this to F_R(max)=mu*m*g because I have no mu, and without that, m appears to be unknown in the T expression. So when it asks:

With what force must the man pull on the rope to reach the speed of 1.5 ms^-1?

How can I do this without the value of m?

It is not your fault if the question hasn't given enough information, but if you show us your working then we can at least tell you if you have proceeded correctly.

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