Solve for Mass: Find Tension of Hanging Object

In summary, to find the mass of the object hanging from the roof, you can use the equations for centripetal force and acceleration, or the equation for centripetal force and the given values for velocity and radius. Once you have the mass, you can then use the equation for tension to calculate the tension in the cord.
  • #1
Willywang
1
0

Homework Statement


you have a object hanging from your roof, once it reaches constant velocity, the diameter of its motion is .755m, and it takes 8.5 seconds to travel 10 cycles. the cord is .46m long

Homework Equations



what is the tension of the cord?
let alone, how do i find the mass of the object?

The Attempt at a Solution



i came up with the equation that T=mx(4)x(pie)^2 x (r)/P^2
but i have everything except for mass in order to solve this.

So..in an attempt to find mass...
i found velocity of the object travels at 2.78 m/s

with F=mv^2/r and A= v^2/r i can substitute F and A in F=ma

but when plugging in numbers, i find that M cancels out each other, leaving me with a dead end.

So, basically if someone can help me find the mass of the object i can solve tension myself

Thanks
 
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  • #2
for sharing your equations and thought process so far. It seems like you are on the right track in terms of using the equations for centripetal force and acceleration to find the mass of the object.

To find the mass, you can rearrange the equation F=ma to solve for m. This would give you the mass in terms of the force and acceleration, which you can calculate using the given diameter and time period.

Another approach you can take is to use the equation for centripetal force, F=mv^2/r, and substitute in the values for velocity and radius to solve for the mass.

Once you have the mass of the object, you can then use the equation for tension, T=mv^2/r, to calculate the tension in the cord. Remember that the velocity in this equation is the tangential velocity, which can be calculated using the diameter and time period.

I hope this helps you solve the problem. Good luck!
 

What is the formula for solving for mass when finding tension of a hanging object?

The formula for solving for mass when finding tension of a hanging object is: m = T/g, where m is the mass of the object, T is the tension force, and g is the acceleration due to gravity (9.8 m/s^2).

How do I determine the tension of a hanging object?

To determine the tension of a hanging object, you must first measure the mass of the object and then use the formula T = mg, where T is the tension force, m is the mass, and g is the acceleration due to gravity. You can also use a spring scale or force sensor to directly measure the tension force.

What units should be used when solving for mass and tension?

The units used for mass should be in kilograms (kg) and the units used for tension should be in Newtons (N). If using the formula T = mg, the units for T will also be in Newtons (N).

Can the tension of a hanging object ever be greater than its weight?

Yes, the tension of a hanging object can be greater than its weight if the object is accelerating. This is because the tension force also includes the force needed to accelerate the object, in addition to the force of gravity pulling the object down.

What factors can affect the mass and tension of a hanging object?

The mass and tension of a hanging object can be affected by various factors such as the strength and length of the rope or string holding the object, air resistance, and the gravitational pull of other nearby objects.

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