A force of 112 N acts on 35 kg box which moves at a steady speed across the floor. The force is directed 40 degrees above the ground. How to state Newton's second law using x components and y components? x: -Fa(cos40) -Ff=ma and y: -Fa(sin40)+Fn-Fg=0? How do you calculate force of friction and normal force from this information? How do you find the force the box is acting on the floor (magnitude and direction)?
To state Newton's second law using x and y components, we can start by decomposing the force acting on the box into its x and y components. The force can be split into two components: Fa(cos40) in the x-direction and Fa(sin40) in the y-direction.
Newton's second law states that the sum of the forces in each direction is equal to the mass multiplied by the acceleration in that direction. Therefore, the x-component of the second law equation becomes:
-Fa(cos40) - Ff = max
Where Ff is the force of friction and ax is the acceleration in the x-direction.
Similarly, for the y-component, the equation becomes:
-Fa(sin40) + Fn - Fg = may
Where Fn is the normal force and Fg is the force due to gravity acting on the box. ay is the acceleration in the y-direction.
Now, let's address how to calculate the force of friction and normal force from the given information.
To calculate the force of friction, we need to know the coefficient of friction (µ) between the box and the floor. The force of friction can be calculated using the formula:
Ff = µ * Fn
Where Ff is the force of friction and Fn is the normal force.
To find the normal force, we can consider the vertical equilibrium of forces. In this case, since the box is moving at a steady speed, there is no vertical acceleration (ay = 0). Thus, the equation for the y-component becomes:
-Fa(sin40) + Fn - Fg = 0
Simplifying this equation, we can isolate the normal force:
Fn = Fg + Fa(sin40)
Now, let's address how to find the force that the box is acting on the floor.
The magnitude of the force that the box is acting on the floor can be found using the Pythagorean theorem:
Magnitude of the force on the floor = √(Ff² + Fa²(sin40)²)
The direction of the force can be determined by finding the angle it makes with the horizontal axis:
Direction of the force on the floor = arctan(Ff / (Fa(sin40)))
By substituting the given values into these formulas, you can calculate the force of friction, normal force, and the magnitude and direction of the force on the floor.