Does force normal change when you push an object at an angle?

[Ace.]

Homework Statement

You exert a force of 131 N [30° below horizontal] onto a 12.6 kg lawn mower, What is the force of gravity and normal force on the lawn mower?

Homework Equations

F_g= m × g
F_{A (y component)} = Sin30° × F_A

The Attempt at a Solution

The force of gravity is equal to the force of normal,
∴ F_N = m × g

= 12.6 kg × 9.8 m/s²​

= 123.48 [up]​

But, the normal force gets added on by the force opposing the y component of the applied force right?

So, F_{A (y component)}Sin30° × F_A

= 65.5 N [down]​

So by Newtons 3rd law there would be a force acting up on the lawn mower of 65.5 N[up].I'm just wondering if these two forces are added to each other for the total normal force which is 123.48 N + 65.5 N = 188.98 N [up]?

 

[Delphi51]

Yes, all correct. The vertical component of the push adds to the weight to make the normal force pressing the mower down on the ground.

 

[Ace.]

Thanks, but I have a question. Why doesn't the force of gravity on the lawn mower increase when you apply your force on it? Aren't you essentially making the lawn mower heavier?

 

[Delphi51]

The force of gravity depends on the MASS of the mower. You probably know it is
Fg = GMm/d² where M is the mass of the Earth and m the mass of the mower.

 

[Nickie]

I can confirm that the normal force does change when an object is pushed at an angle. The normal force is the perpendicular force exerted by a surface on an object in contact with it. When an object is pushed at an angle, the normal force is not only dependent on the object's weight, but also on the component of the applied force perpendicular to the surface. In this case, the normal force will be greater than the object's weight because there is an additional component of the applied force acting perpendicular to the surface.

To calculate the normal force in this scenario, we can use the formula: FN = mg + Fsinθ, where F is the applied force, θ is the angle at which the force is applied, and m is the mass of the object. In this case, the normal force would be:

FN = (12.6 kg)(9.8 m/s^2) + (131 N)(sin30°)
= 123.48 N + 65.5 N
= 188.98 N [up]

So, in conclusion, the two forces are not added together to determine the total normal force. Instead, we must consider the components of the applied force and use the formula to calculate the normal force.