a boom 4.7 meters,10000 kg, 20 degree angle, find torqe on the pivot

i fond force=10000x9.81= 98100 N
perpindiclar force = 33552 N
torqe = 4.7x33552 = 167695 Nm

i am told this is wrong

toque = 98,100 * 4.7 * cos 20 = 433,264 N m

I think you used sin and not cos
and you have a typo anyway, should be 157,695 N m

Your sin assumption would be correct if your 20 deg boom angle is from vertical, but usually you measure from horizontal.

To find the torque on the pivot, you need to consider both the force applied and the perpendicular distance from the pivot point. Let's break down the process step by step:

Step 1: Calculate the force applied
You correctly calculated the force applied as the weight of the boom, which is mass multiplied by the acceleration due to gravity. Therefore, the force applied is:
Force = 10000 kg * 9.81 m/s² = 98100 N

Step 2: Calculate the perpendicular force
To calculate the perpendicular force, you need to find the component of the force that acts perpendicular to the boom. This can be done using trigonometry. Since the angle given is 20 degrees, we can calculate the perpendicular force as follows:
Perpendicular force = Force * sin(angle)
Perpendicular force = 98100 N * sin(20°) ≈ 33555 N (rounded to the nearest whole number)

So, your calculation for the perpendicular force is correct.

Step 3: Calculate the torque
Finally, to find the torque on the pivot, you need to multiply the perpendicular force by the perpendicular distance from the pivot. In this case, the given distance of the boom is 4.7 meters. Therefore, the torque can be calculated as follows:
Torque = Perpendicular force * perpendicular distance
Torque = 33555 N * 4.7 m ≈ 157674 Nm (rounded to the nearest whole number)

It seems you made a slight error in multiplying the perpendicular force by the distance. The correct torque is approximately 157674 Nm, not 167695 Nm as you initially calculated.

Remember to double-check your calculations and units to ensure accuracy.