Incline plane + torque problem

In summary: You can work out the angle by using the V=I*A equation. So the angle is (0.4*3*a*0.5), or 14 degrees. Now it's time to solve the equation for the CoM. To do this, you need to use the Chain Rule. The Chain Rule states that if you have two forces (F1 and F2) and you want to find the third force (F3), you can write F3 = (F1*F2)/(1+F2). In this case, F1 and F2 are the forces acting on the block and 0 is the force of gravity. So, F3 = (0.4*
  • #1
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Homework Statement


A tall uniform rectangular block sits on an inclined plane. If Us = .4, does the block slide or fall over as the angle is slowly increased? Also, the block is 3a units tall and "a" units wide.


The Attempt at a Solution


Just by intuition, I figured that it would tip over, since the static friction is pretty high, but I'm not sure how to prove that.

I initially thought you could say that as the incline increased, the force between the bottom of the block and the incline plane would increase, creating torque on the block. But in this case, there's no opposing torque at the top of the block, so by this logic, it would tip over as soon as there was any incline. Any help would be appreciated. Thanks!
 
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  • #2
This is a statics problem. You want to analyze the point where nothing is moving (everything is "static") but if you were to increase the incline any further the block would either tip or slide.

Anytime you have to solve a statics problem you should immediately think of two things:
1) Sum of forces equals zero
2) Sum of torques equals zero

Solving every statics you will see will probably go the same way:
* Find an expression for the sum of forces along a particular axis. Set it equal to zero. (Remember to choose your coordinate axes so that most or all forces will be along one axis.)
* Find an expression for the sum of torques. Set it equal to zero.
* Solve the equations that you just wrote down.

So the first step to solving any statics problem involves identifying all the potential sources for torques and/or forces. In this problem the forces are: gravity, friction, normal force.
 
  • #3
Thinking of your block slowly tipping over - it will fall when the centre of mass goes just past the point directly over the point of contact. This should be calculable, which gives you an angle. You can then work out the frictional force vs the sliding force.
In the little pic, the red dot represents the CoM.
 

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1. How do you calculate the torque of an object on an inclined plane?

To calculate the torque of an object on an inclined plane, you will need to know the force acting on the object, the distance from the pivot point to the line of action of the force, and the angle between the force and the inclined plane. The torque can be calculated using the formula: torque = force x distance x sin(angle).

2. How does the angle of the incline affect the torque on an object?

The angle of the incline can greatly affect the torque on an object. The greater the angle, the higher the torque will be. This is because the component of the force acting perpendicular to the plane (which creates torque) increases as the angle increases. Additionally, the distance from the pivot point to the line of action of the force decreases as the angle increases, further increasing the torque.

3. What is the relationship between the weight of an object and the torque on an inclined plane?

The weight of an object does not directly affect the torque on an inclined plane. However, the weight of an object can be broken down into its components (perpendicular and parallel to the plane), and the perpendicular component will contribute to the torque. Therefore, a heavier object with a greater perpendicular component of weight will have a higher torque on an inclined plane.

4. How does friction impact the torque on an object on an inclined plane?

Friction can have a significant impact on the torque of an object on an inclined plane. Friction works against the motion of the object and creates a counteracting torque. The amount of friction will depend on the coefficient of friction between the two surfaces in contact and the normal force acting on the object. A higher coefficient of friction or a higher normal force will result in a greater frictional torque.

5. Can the torque on an object on an inclined plane ever be zero?

Yes, the torque on an object on an inclined plane can be zero. This will occur when the object is at equilibrium, meaning that the net torque acting on the object is zero. In this case, the forces acting on the object are balanced and there is no motion or rotation. The angle of the incline, the weight of the object, and the frictional force (if present) must all be in specific ratios to achieve equilibrium and a net torque of zero.

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