Statics: Equilibrium and circular lawn roller

[TranceMaster]

1. What horizontal force F will pull the 100 kg lawn roller over the step? What is the value of F if it is directed normal to AC?

I can't draw a picture for you, but i can describe it. There is a circular lawn roller in contact with a step that is 3cm in height. The roller is currently resting on the ground. the radius of the roller is 30 cm. I initially need to find a force in the horizontal direction, then find a force that is 45 degrees up from that. You can mark the top of the step as point A and the center of the roller as point C. Both forces start from C.

Homework Equations

sum F = 0
sum M = 0

The Attempt at a Solution

I tried solving for the force in both the X and Y directions. My professor gave me the hint that as the roller is goin up the step, the normal force will end up disappearing from the ground to the step. This however, still has me confused. He told me that i will have 2 unknowns and 2 equations. I have the equations, but I am uncertain of what I am doing to get the force.

 

[Doc Al]

Hint: As the roller climbs the step it must rotate about the edge of the step. Consider torques about that point.

 

[baba89]

I would approach this problem by first identifying all the given parameters and the unknowns. In this case, the given parameters are the weight of the lawn roller (100 kg), the height of the step (3 cm), and the radius of the roller (30 cm). The unknowns are the horizontal force F and the force directed normal to AC.

Next, I would draw a free body diagram of the lawn roller, showing all the forces acting on it. In this case, there are three forces: the weight of the lawn roller acting downward, the normal force from the ground acting upward, and the force F acting horizontally. Since the lawn roller is in equilibrium, the sum of all the forces must be equal to zero.

Using the equations of sum F = 0 and sum M = 0, I would set up two equations to solve for the two unknowns. In the first equation, I would set the sum of forces in the x-direction equal to zero. This would give me:

F - N = 0

Where N is the normal force from the ground. In the second equation, I would set the sum of moments about point C (the center of the roller) equal to zero. This would give me:

F(0.3 m)sin(45°) - N(0.3 m)cos(45°) - (100 kg)(9.8 m/s^2)(0.3 m)cos(45°) = 0

Where the first term represents the moment of the force F, the second term represents the moment of the normal force, and the third term represents the moment of the weight of the roller.

Solving these two equations simultaneously would give me the value of F, which is the horizontal force needed to pull the lawn roller up the step. To find the force directed normal to AC, I would simply use the Pythagorean theorem to find the magnitude of this force, which would be equal to N.

It is important to note that the direction of the force F is not specified in the problem, so it could be directed at any angle. However, if we assume that the lawn roller is being pulled straight up the step, then the direction of F would be 45 degrees up from the horizontal.