Max Tangential Speed of Mass Before Cord Breaks

In summary, the conversation discusses a scenario where a mass of 2.47 kg is attached to a string and slides without friction on a horizontal surface. The maximum tangential speed the mass can have before the cord breaks is 4.33 m/s. In a second scenario, the same mass is whirled in a vertical circle with a new string and a radius of 0.410 m. The magnitude of the tension at the top is 2.45×102 N when the speed at the top is 6.69 m/s. There is some confusion on the method used to calculate the tension in the second scenario, as gravity must also be taken into account.
  • #1
MutTurwen
3
0
A mass M of 2.47 kg is attached to the end of a string whose length is 0.410 m. The mass slides without friction on a horizontal surface as indicated in the diagram.

a)If the string can withstand a maximum tension of 113.1 N, what is the maximum tangential speed the ball can have before the cord breaks?
Answ: 4.33 m/s

b)The mass, with a new string, is whirled in a vertical circle of the same radius about a fixed point. Find the magnitude of the tension when the mass is at the top if its speed at the top is 6.69 m/s.
Answ: 2.45×102 N


For part a) i used the formulaa 1) F=ma 2)a=rw^2 3) V=rw to get the right answer but for part b) I used 1)V=rw 2) a=rw^2 3)T=ma but I am not getting the right answer. Am I doing something wrong?
 
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  • #2
Diagram please.

BJ
 
  • #3
b) the motion is vertical, so you must take gravity into account.
 
  • #4
In the second case, gravity is also acting.
So, mv^2/r=mg+T.
 
  • #5
T = m ((v^2/r)-g)
 

1. What is the "Max Tangential Speed of Mass Before Cord Breaks"?

The "Max Tangential Speed of Mass Before Cord Breaks" refers to the maximum speed at which a mass can rotate before the cord holding it breaks. It is an important factor in understanding the limits and capabilities of various systems, such as centrifuges and pendulums.

2. How is the "Max Tangential Speed of Mass Before Cord Breaks" calculated?

The calculation for the "Max Tangential Speed of Mass Before Cord Breaks" involves several factors, including the strength and material of the cord, the weight and shape of the mass, and the length of the cord. It can be determined using the formula: V = √(g * L), where V is the maximum tangential speed, g is the acceleration due to gravity, and L is the length of the cord.

3. Why is the "Max Tangential Speed of Mass Before Cord Breaks" important in scientific research?

The "Max Tangential Speed of Mass Before Cord Breaks" is important in scientific research because it helps scientists understand the limitations of various systems and how they can be improved. It also plays a crucial role in ensuring the safety and functionality of equipment that involves rotating masses, such as amusement park rides and industrial machinery.

4. How does the "Max Tangential Speed of Mass Before Cord Breaks" affect the performance of centrifuges?

The "Max Tangential Speed of Mass Before Cord Breaks" is a critical factor in the performance of centrifuges, as it determines the maximum speed at which samples can be spun without causing the cord to break. This speed is often referred to as the "maximum g-force" and is essential in achieving accurate and efficient separation of substances in scientific experiments and medical procedures.

5. Can the "Max Tangential Speed of Mass Before Cord Breaks" be increased?

Yes, the "Max Tangential Speed of Mass Before Cord Breaks" can be increased by using a stronger and more durable cord or by reducing the length of the cord. However, it is important to note that increasing the speed also increases the amount of force applied to the mass and the cord, so safety precautions must be taken into consideration.

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