Net Torque: Determine Magnitude from Ladder Base

[nickb145]

Homework Statement

A 17m long ladder is mounted on a fire truck. The ladder itself has mass 130kg , and at the top is a 37kg basket holding a 83kg firefighter.

If the ladder makes a 60∘ angle with the horizontal, what's the magnitude of the net torque about the ladder's base?

Homework Equations

I think center of mass (X1M1+X2M2+X3M3)/(m1+m2+m3)
Torue=rFsinθ

The Attempt at a Solution

I get a huge number when i try it out. But since is is asking about the ladders base, would it the sine change to cosine?

I take the torque from the mass at the end and the torque of the ladder to get the net torque. Kind of stuck.

 

[rude man]

Never mind "center of mass of all the forces."

You have the center of mass of 130 kg of the ladder at 8.5m from the pivot axis. You have 120 kg of mass at 17m from the pivot point. You have a 60 deg. angle with the horizontal.

Compute the torques due to the ladder mass and the basket cum firefighter.

 

[nickb145]

Ok then so it is just

Tnet=(8.5)(9.8)(130)Sin(60)+(17)(9.8)(120)Sin(60)

 

[rude man]

Why sin?

 

[Nickie]

I would first clarify any assumptions or unknowns in the problem statement. For example, it is not specified where the ladder is mounted on the fire truck, which could affect the calculation of the net torque. I would also double check the units and ensure they are consistent throughout the problem.

To determine the magnitude of the net torque about the ladder's base, we can use the equation for torque: T = rFsinθ, where r is the distance from the base of the ladder to the point where the force is applied, F is the force applied, and θ is the angle between the force and the lever arm (in this case, the ladder). We can also use the equation for the center of mass (COM) to determine the distance r.

To find the center of mass of the ladder and the basket, we can use the equation COM = (X1M1+X2M2+X3M3)/(m1+m2+m3), where X is the distance from the base of the ladder to each object's center of mass, and M is the mass of each object. We can then use the COM as the distance r in the torque equation.

However, as the ladder is at a 60 degree angle, the force of gravity acting on the ladder and the basket will not be perpendicular to the ladder. Therefore, the torque calculation will need to take into account the component of the force that is perpendicular to the ladder. This can be done by using the sine of the angle between the force and the ladder, as you have correctly stated.

To find the net torque about the ladder's base, we can add the torques from each object (ladder, basket, and firefighter) together. Keep in mind that the torque from the firefighter will be in the opposite direction as the torque from the ladder and basket, due to the angle of the ladder.

Once all the torques have been calculated, we can add them together to find the net torque about the base of the ladder. This will give us the magnitude of the net torque. It is important to note that the direction of the net torque will be determined by the direction of the forces and the angle of the ladder.

In summary, to determine the magnitude of the net torque about the ladder's base, we must first calculate the center of mass of the ladder and the basket, then use the torque equation to find the torque from each object, and finally add all