simple swing problem and centripetial force

[nickelbackfan]

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A 5m massless string is set up with a mass of 5 kg on the end. The mass is swung like a pendulum and at its maximum amplitude reaches 90° to either side of its resting position. What is the maximum tension generated on the string during its swing?




Answer is 150

I understand that at the bottom of the swing there is gravity and also centripetal force, but I was under the impression that the centripetal force acts in the opposite of gravity (pulling in ward). Am I wrong or are they just asking for the magnitude?

Thanks

 

[shaboobly]

newton's 3rd law i think applies. you have the centripetal force towards the center of the circle, but since at this point the mass is not accelerating (well it is cause there is centripetal force but idk how to explain better 🙂) there is tension in the string equal to the centripetal force plus the weight of the mass.

 

[nickelbackfan]

newton's 3rd law i think applies. you have the centripetal force towards the center of the circle, but since at this point the mass is not accelerating (well it is cause there is centripetal force but idk how to explain better 🙂) there is tension in the string equal to the centripetal force plus the weight of the mass.

So from the mass's point of view, there is gravity pulling downwards and centripetal force upwards, and from the strings point of view that centripetal force is downward?

 

[shaboobly]

gravity is not a force, weight is. the weight adds to the tension of the string. the centripetal force is directed towards the center of the circle always and according to newton's third law, to every force there is an equal and opposite force. in terms of the questions it seems they just want the maximum magnitude, so solve from here. you need to remember to always break up your forces and see what is going on.

 

[indianjatt]

At the bottom of the swing is when you have maximum tension. Here, the velocity will be sq root 2gh. Since we are dealing with a pendulum, we know the NET force will be equal to the centripetal force. At the bottom of the swing (at equilibrium), we have gravity acting downwards and the tension of the string action upwards.

Tension - Fgravity = Fnet
Fnet = 5 kg(2*10*5) / 5 = 100 N.

Tension = F Gravity + 100 N = 5 kg * 10m/s^2 + 100N = 150N.