Problem about torque?

Question

a 10-m uniform beam has a mass of 260kg. the following weights are acting on it: 4000N at 2.0m from the left end, 3000N at 6.0m from the left end and 2000N at 1.0m from the right end. what are the magnitude of forces T1 and T2 acting on two ends of the beam to keep it in equilibrium? solution please

Answer 1

Sum the 3 moments and the m x a at the center of the beam for both point T1 and T2, as separate calculations.

Answer 2

Lets say t1 is acting in the left end, and t2 in the right end of the beam.

The mass of the beam is 260kg, to convert it to a force, we multiply it by 9.8 (gravity acceleration constant), and its 2548N acting in the middle of the beam.

We do the sum of vertical forces

T1 + T2 = 2548N + 4000N + 3000N + 2000N

T1 + T2 = 11548N

We do a sum of momentum at any of the two unknown values, lets say at T1

0 = -2548(5) - 4000(2) - 3000(6) - 2000(9) + T2(10)

T2= 5674 N

Now that we have T2, we can go to the first equation and find T1

T1= 5874 N

T2= 5674N