Using Newton's laws to solve problems

[juliesangelcleo]

Homework Statement

"while moving in a homeowner is pushing a box across the floor at a constant velocity. The coefficient of friction is .41. The pushing force is directed in a downward motion at and angle of theta below the horizontal. When theta's value is greater then a certain value, then the box can not be moved, no matter the force. What is this theta.

I don't know how to start this one.

 

[denverdoc]

You know that a FBD, and a list of potentially useful eqns is a great way to start. Assuming you have done that, what is the normal force here (the force with which the floor pushes back). From there its easy to get the frictional force. The push must of course be resolved into X and Y components.

 

[m2003]

I would approach this problem by first understanding and applying Newton's laws of motion. The first law states that an object will remain at rest or in motion with a constant velocity unless acted upon by an external force. In this case, the box is being pushed with a constant velocity, meaning that the net force acting on it is zero.

The second law states that the net force on an object is equal to its mass multiplied by its acceleration. In this case, the box is not accelerating, so the net force must be zero. This means that the pushing force must be equal and opposite to the force of friction acting on the box.

Using the formula for friction, Ff = μN (where μ is the coefficient of friction and N is the normal force), we can set up an equation to find the normal force of the box. Since the box is not moving vertically, the normal force must be equal to the weight of the box (mg).

Next, we can use trigonometry to determine the components of the pushing force in the horizontal and vertical directions. The vertical component (Fv) will be mgcosθ and the horizontal component (Fh) will be mgsinθ.

Since we know that the net force must be zero, we can set up an equation: Fh - Ff = 0. Substituting in the values we found for Fh and Ff, we get mgsinθ - μ(mgcosθ) = 0. Simplifying, we get tanθ = μ.

From this equation, we can see that when the angle θ is greater than the inverse tangent of the coefficient of friction (tan⁻¹(μ)), the box will not be able to be moved, no matter the force applied. This is because the pushing force will not be enough to overcome the force of friction acting on the box.

In conclusion, by applying Newton's laws of motion and using trigonometry, we can determine that the angle θ must be greater than tan⁻¹(μ) in order for the box to not be able to be moved.