Find the tension in the rope.

In summary, a 212-kg log is being pulled up a ramp with an incline of 29.1° using a rope parallel to the surface. The coefficient of kinetic friction is 0.757 and the log has an acceleration of 0.720 m/s2. To find the tension in the rope, the formula F=ma is used, along with the normal force and the relationship between the resistive force and the normal force. A free-body diagram can also be helpful in visualizing the forces involved.
  • #1
black02
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A 212-kg log is pulled up a ramp by means of a rope that is parallel to the surface of the ramp. The ramp is inclined at 29.1° with respect to the horizontal. The coefficient of kinetic friction between the log and the ramp is 0.757, and the log has an acceleration of 0.720 m/s2. Find the tension in the rope.



Fx=ma(of x)
Fy=ma(of y)

i know i have a normal force

this is what i have but i am stuck

how do i set this up?
 
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  • #2
black02 said:
Fx=ma(of x)
Fy=ma(of y)

i know i have a normal force

this is what i have but i am stuck

how do i set this up?

You have a block on a ramp. <--[BLOCK]-->

Those (<--) are vectors. They are pointing in opposite directions. One of them is a pulling force and one is a resistive force. The resistive force and the normal force have a relationship which you can use.

Hope this was helpful.
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  • #3
i have come back to it. this is what i have so far.

force of friction = .757*185.24
f=140.227
i got this using this formula

f = mkn

f = Force of Friction.
mk = Coefficient of kinetic friction.
n = The normal force pressing the surfaces together.

however the object is still accelerating so the tension force is greater just not sure how i get the tension force from this.
 
  • #4
black02 said:
i have come back to it. this is what i have so far.

force of friction = .757*185.24

This is close. But the forces in the Y direction are N - mg cos 29.1 = 0. You have them as N - m cos 29.1 = 0, so your value for the normal force (and therefore the frictional force) are too low.

ihowever the object is still accelerating so the tension force is greater just not sure how i get the tension force from this.

Have you drawn a free-body diagram? Those help me a lot. You will have an arrow up the incline for T, the tension in the rope. And you will have arrows downward, along the incline for the friction and gravity. These represent vectors, which add up to the total force created by the accelerating mass of the log.

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1. What is tension?

Tension is a force that is transmitted through a rope, string, or cable when it is pulled tight by forces acting from opposite ends.

2. How is tension calculated?

Tension is calculated by multiplying the mass of the object by the acceleration due to gravity, and then adding any other forces acting on the object.

3. What factors affect the tension in a rope?

The factors that affect the tension in a rope include the mass of the object, the acceleration due to gravity, the angle of the rope, and any other forces acting on the object.

4. How do you measure tension in a rope?

Tension can be measured using a spring scale or a force meter, by attaching it to the rope and pulling in opposite directions until the rope is taut.

5. What are some real-life applications of tension in ropes?

Some real-life applications of tension in ropes include rock climbing, zip lining, and construction of suspension bridges and cranes.

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