Finding force exerted by a rope and ratio of tension:weight

You found the force exerted by the rope in kN, but her weight is given in kg. Convert her weight to Newtons (W=mg) and then find the ratio by dividing the force exerted by the rope by her weight. In summary, the problem involves an ice skater moving in a circle while holding onto a rope attached to a pole. The force exerted by the rope on her arms is 2.3886108 kN and the ratio of this tension to her weight is 0.003348. However, the ratio is incorrect because the units of the two forces must be the same. Converting the skater's weight to Newtons and then finding the ratio gives the correct answer.
  • #1
iamjohnny56
10
0

Homework Statement



A 72.8 kg ice skater is moving at 5.01 m/s when she grabs the loose end of a rope, the opposite end of which is tied to a pole. She then moves in a circle of radius 0.765 m around the pole.

The acceleration of gravity is 9.8 m/s2 .
Find the force exerted by the rope on her arms.
Answer in units of kN = 2.3886108 kN

Find the ratio of this tension to her weight.

Homework Equations



Fc = mv^2 / R
W=mg

The Attempt at a Solution



Fc = mv^2 / R
Fc = (72.8)(5.01)^2 / .765
Fc = 2388.6108 N
Fc = 2.3886108 kN

It's the ratio that's getting me, shouldn't it just be:
2.3886108 kN / (72.8 x 9.8)
=.003348

But the ratio is wrong?

Please help.
 
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  • #2
The ratio is a comparison of two forces. But they must be in the SAME units!
 

FAQ: Finding force exerted by a rope and ratio of tension:weight

1. What is the force exerted by a rope?

The force exerted by a rope is the amount of pulling or pushing force that the rope applies on an object. It is typically measured in Newtons (N) or pounds (lbs).

2. How is the force exerted by a rope calculated?

The force exerted by a rope can be calculated using the formula F = m x a, where F is the force, m is the mass of the object, and a is the acceleration. The force exerted by the rope is equal and opposite to the force exerted by the object on the rope.

3. What is the ratio of tension to weight in a rope?

The ratio of tension to weight in a rope is the relationship between the force applied on the rope (tension) and the weight of the object it is supporting. It is typically expressed as a decimal or a percentage.

4. How can the ratio of tension to weight be measured?

The ratio of tension to weight can be measured by using a spring scale or a dynamometer to determine the tension in the rope, and then dividing it by the weight of the object being supported by the rope.

5. What factors affect the ratio of tension to weight in a rope?

The ratio of tension to weight in a rope is affected by the weight of the object, the angle of the rope, and the properties of the rope itself (such as its elasticity and thickness). The ratio will also change if the weight or angle of the rope is altered.

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