Question

What is the sum of all torques in the system above?
Round your answer to 2 decimal places.

Answer 1

The torque about the origin of the given force is -6.0î - 14.0ĵ - 12.0k Nm.

Step-by-step explanation:

The torque about the origin can be calculated using the formula:

T = r x F

where r is the position vector and F is the force vector.

Given r = (-2.0î + 4.0ĵ) m and F = (5.0î - 2.0ĵ + 1.0k) N, we can calculate the torque as follows:

T = (-2.0î + 4.0ĵ) x (5.0î - 2.0ĵ + 1.0k)

Using the cross product formula:

T = (0.0 + 2.0 - 8.0)î + (-10.0 + 0.0 - 4.0)ĵ + (-2.0 - 10.0)k

T = -6.0î - 14.0ĵ - 12.0k

So, the torque about the origin of the given force is -6.0î - 14.0ĵ - 12.0k Nm.

Answer 2

8.33Nm

Step-by-step explanation:

First identify the forces that you want positive and negative, in this case I chose blocks 1 and 2 to be positive and 3 to be negative. This would give you T = (F1*r1) + (F2*r2) - (F3*r3). Plug in the numbers and you get T = (19.6N * 0.4m) + (9.8N * 0.2m) - (4.9N * 0.3m). Simplify that and you get T = 7.84+1.96-1.47. T = 8.33Nm