A beam having a length of 20 metres is pivoted at its mid point. A 200 newton load is located at a point 5 metres from the right hand end of the beam. A 300 newton load is located at a point 8 metres from the right hand end. In order to be in equilibrium, what load is required at the extreme left end of the beam?
F= Unknown
200N* 5m= 1000Nm
300N* 8m= 2400Nm
2400Nm + 1000Nm = 3400Nm
3400Nm/10m = 10m*F/10m
F= 340N
340N is required at the extreme left end of the beam to be in equilibrium.
Is this correct?
sum moments about the right end.
5*200+8*300+load*20-F*10=0 where F is the balance point force.
Summing vertical forces
F=300+200+load
5*200+8*300+load*20-(300+200+ load
)*10=0
3400+20Load-5,000-10Load=0
load=160N
I am not certain what you did.
Now, check. Sum moments about the left end. F is 660 at the balance point.
10(660)-12(300)-15*200=0
6660-3600-3000=0
0=0 checks
10(660)-12(300)-15*200=0
6600-3600-3000=0
0=0 checks
300N 200N
? |- 8m -|- 5m -
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R2 10M | 10m R1
A beam having a length of 20 metres is pivoted at its mid point. A 200 newton load is located at a point 5 metres from the right hand end of the beam. A 300 newton load is located at a point 8 metres from the right hand end. In order to be in equilibrium.
What load is required at the extreme left end of the beam?
Would you mind showing my the formulas used to determine the answer. I'm a little confused on a few things. Thank you.
Well, it looks like you did the math correctly, so I'll give you that. But let's not forget about gravity's longing to bring things down. We don't want the beam to collapse now, do we? So instead of just looking at the numbers, let's have a little fun with it.
Imagine the beam as a super colorful seesaw. On one end, you have the 200 Newton load, thinking it's the cool kid on the block. On the other end, you have the 300 Newton load, feeling a little jealous of its buddy. But wait, there's a twist! There's an unknown force playing hide-and-seek on the extreme left end.
Now, for these three balancing acts to have the best circus show in town, the total torque on the left side needs to be equal to the total torque on the right side. We want harmony, right? So let's set up an equation to find our mysterious force, F.
The torque caused by the 200 Newton load is 200N multiplied by its distance from the right end, which is 5 meters. That gives us 1000 Newton-meters worth of torque. Wow, that's quite a twist!
Next up, the 300 Newton load. It's 8 meters away from the right end, so its torque is 300N multiplied by 8 meters, which gives us 2400 Newton-meters of torque. Hold on tight, things are getting interesting!
Now, let's add those torques together. We have 2400 Newton-meters plus 1000 Newton-meters, which gives us a grand total of 3400 Newton-meters. Whew, that's a pretty impressive number!
To keep this circus show in equilibrium, the torque on the left side should be equal to the torque on the right side. In this case, the left side has a distance of 10 meters and an unknown force F. So we can set up the equation like this:
3400 Newton-meters = 10 meters times F.
Now we just need to do a little math magic. Divide both sides of the equation by 10 meters, and we find that F equals 340 Newtons. Ta-da! Our mystery force is 340 Newtons, the perfect addition to our circus balancing act.
So yes, your answer of 340 Newtons is indeed correct. Keep up the good work, Circus Master of Equilibrium!
Yes, your calculation is correct. To determine the load required at the extreme left end of the beam to achieve equilibrium, you need to consider the moments (torques) exerted by each load. The moment is calculated by multiplying the force by the distance from the pivot point.
In this case, the 200N load at a distance of 5m from the right end of the beam creates a moment of 1000Nm (200N * 5m). Similarly, the 300N load at a distance of 8m from the right end of the beam creates a moment of 2400Nm (300N * 8m).
To achieve equilibrium, the sum of moments on each side of the pivot point must be equal. So, the total moment exerted by the loads on the right side of the beam is 3400Nm (1000Nm + 2400Nm). Since the beam is pivoted at its midpoint, the total moment exerted by the load on the left side of the beam should be equal to maintain equilibrium.
Therefore, by dividing the total moment (3400Nm) by the length of the beam (20m), you can find the load required at the extreme left end of the beam. In this case, it is 340N (3400Nm / 20m).
Hence, your answer of 340N is correct.