Solving Torque Rock Problem: Force, Location & Equations

[aeroengphys]

Homework Statement

Someone places a 6.0m long steel rod on a rock so that one end is under a baby moose weighing 2.0 kN. THe person pushes down on the other end of the rod with a force of 400N, and the moose is held in the air at rest. The rock was:
(a) 1.0m from the moose
(b) 5.0m from the moose
(c) 1.0m from the person
(d) 6.0m from the person
(e) none of these

Homework Equations

T = Fl
Tnet = 0
Fnet = 0

The Attempt at a Solution

So I began this problem by drawing a free body diagram. I drew the 2000N moose on the right end of a rod that is balanced in the center by a rock. I drew that there are two forces acting in the downward direction, the 400N force and the 2000N W. Since I don't know the force applied on the rod by the rock, I made the center of gravity my axis of rotation. My teacher gave us the answers at the end of class, and said that the answer is (a). Is this because of the ratio between the forces of the moose and the person? How do you know that there's a relationship between the force applied and the location to which it's applied? Thanks in advance.

 

[berkeman]

The torques are summed about the fulcrum for a lever. The rock is the fulcrum in this example.

 

[m2003]

I would like to first commend you for your approach to this problem. Drawing a free body diagram and considering the forces and their locations is a good start.

To solve this problem, we need to consider the concept of torque, which is the force applied at a distance from the axis of rotation. In this case, the axis of rotation is the center of the rod. The torque equation is T = Fl, where T is the torque, F is the force, and l is the distance from the axis of rotation.

In order for the rod to remain in equilibrium, the net torque on the rod must be zero. This means that the torque applied by the person pushing down on the rod (T1 = 400N x l1) must be equal and opposite to the torque applied by the moose (T2 = 2000N x l2).

So, we can set up the equation T1 = T2 and solve for the distance l2. Since we are given the distance l1 as 1.0m, we can plug that in and solve for l2. This gives us l2 = 5.0m, which is the answer (b) in the given options.

To answer your question about the relationship between the force applied and its location, torque is directly proportional to both the force and the distance from the axis of rotation. This means that if the force applied remains constant, increasing the distance from the axis of rotation will increase the torque. So in this problem, the person needs to apply a larger force at a shorter distance (1.0m) to balance the torque applied by the moose at a longer distance (5.0m).

I hope this explanation helps in understanding the relationship between force, location and torque in solving this problem. Keep up the good work in approaching problems in a scientific manner.