How Much Mass is Needed for a Counterweight to Balance a Truck on an Incline?

[xdevinx]

Homework Statement

Find the mass m of the counterweight needed to balance the 1600 kg truck on the incline. Assume all pulleys are frictionless and massless.

Picture attached

Homework Equations

Conditions for static equilibrium so that angular acceleration=0:
$$\sum$$Torque=0

The Attempt at a Solution

We're learning about rotational dynamics and torque and I honestly cannot make the connection between that and this problem. Please help ):

 

[tiny-tim]

Welcome to PF!

Find the mass m of the counterweight needed to balance the 1600 kg truck on the incline. Assume all pulleys are frictionless and massless.
…
We're learning about rotational dynamics and torque and I honestly cannot make the connection between that and this problem. Please help ):

Hi xdevinx! Welcome to PF!

I can't see the diagram yet, but if this is a standard weight-pulley-weight problem, then rotational dynamics and torque and irrelevant …

just call the tension T, and use good ol' Newtons second law twice (once on each weight).

 

[nlightner]

I understand your confusion and I am here to help. In this problem, we are dealing with static equilibrium, which means that the truck is not moving. This means that the sum of all forces and torques acting on the truck must be equal to zero. In order for the truck to be in equilibrium, the torque due to the weight of the truck must be balanced by the torque due to the counterweight.

To find the mass of the counterweight needed, we can use the equation for torque: T = r x F, where T is the torque, r is the distance from the pivot point to the point of application of the force, and F is the force acting on the object. In this case, the pivot point is at the bottom of the incline and the force is the weight of the truck. The distance r can be calculated using trigonometry.

Once we have the torque due to the weight of the truck, we can set it equal to the torque due to the counterweight and solve for the mass m. This will ensure that the truck is in static equilibrium and will not roll down the incline.

In summary, we can use the principles of static equilibrium and torque to determine the mass of the counterweight needed to balance the truck on the incline. I hope this helps and feel free to ask any further questions if needed.