Calculate Tension in 5m String Attached to 4kg Bob

In summary, the tension in the string attached to a 4 kg bob moving in horizontal circles of 0.6 m radius can be calculated using the equation T= m*g/cosα, where α is the angle of the string. After correcting the calculation for α, the correct value for T is 321.65 N.
  • #1
John78
21
0

Homework Statement



Calculate the tension in a 5 m string attached to a 4 kg bob that is moving in horizontal circles of 0.6 m radius.


Homework Equations





The Attempt at a Solution



α= tan-1 0.6/5
= 7 degree

T cos α = m*g

T= m*g/cosα

T=4*9.8/0.12

T=326.6 N



I just want to check whether my working is correct or not.
 
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  • #2
Your equations are almost correct, however, if the angle α is 7 degrees, then cos α = cos 7 = ? But your calc for that angle is not right. It is not the tan function per your attempt...
 
  • #3
so am I right in my calculations

α= sin 0.6/5
= 7 degree = 0.121869343

T cos α = m*g

T= m*g/cosα

T=4*9.8/0.121869343

T=321.65N
 
  • #4
John78 said:
so am I right in my calculations

α= sin^-1 0.6/5 = sin^-1 0.12
α = 6.9 degrees


T cos α = m*g

T= m*g/cosα
yes
T=4*9.8/0.121869343
No, the cosine of 6.9 degrees is not 0.121869343
 
  • #5
cos 6.9 = 0.992757341

Am I right?
 
  • #6
John78 said:
cos 6.9 = 0.992757341

Am I right?
yes, so T = ?
 

FAQ: Calculate Tension in 5m String Attached to 4kg Bob

What is tension and how is it calculated?

Tension is a force that is exerted on an object by a string, rope, or other material. It is calculated by dividing the weight of the object by the length of the string or rope that is supporting it.

How is tension related to the weight and length of the object?

Tension is directly proportional to the weight of the object and inversely proportional to the length of the string or rope. This means that as the weight of the object increases, the tension increases, and as the length of the string or rope increases, the tension decreases.

What is the formula for calculating tension?

The formula for calculating tension is T = (m * g) / L, where T is tension, m is the mass of the object, g is the acceleration due to gravity (9.8 m/s^2), and L is the length of the string or rope.

How do I calculate tension in a 5m string attached to a 4kg bob?

To calculate the tension in a 5m string attached to a 4kg bob, plug in the values into the formula: T = (4kg * 9.8 m/s^2) / 5m = 7.84 N. This means that the tension in the string is 7.84 Newtons.

What units are used to measure tension?

Tension is typically measured in units of force, such as Newtons (N) or pounds (lbs). It can also be measured in units of mass multiplied by acceleration, such as kilograms (kg) multiplied by meters per second squared (m/s^2).

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