# Newton's Law: Angled applied force and friction

• Starry
In summary, to find the force required to maintain constant velocity while pushing a lawnmower, the boy must apply a force of 168N at an angle of 35 degrees below the horizontal. This is found by calculating the components of the applied force, using the equations for net force and friction, and using the Pythagorean theorem to find the total force.
Starry

## Homework Statement

A boy is pushing a lawnmower (25kg) with 200N of force on a handle that is angled 35 below the horizontal. The mower is accelerating at 0.9m/s^2. If the boy would like to maintain a constant velocity, what force does he need to apply to the mower handle.
Assume g = 9.8 [d]

## Homework Equations

Fnet = ma
Fnet = Fapp + Ffr
Ffr = FN * μ

## The Attempt at a Solution

To find the components of the 200N force [35 degrees above horizon], I simply draw out the triangle and use sin and cos to find it. I found:
Fx = 200cos35 = 163.83N [forward]
Fy = 200sin35 = 114.71N [down]

Since it's accelerating, there is a net force. Using the two following equations,
Fnet = ma
Fnet = Fapp + Ffr
(25)(0.9) = Ffr + Fx
(25)(0.9) = Fn * μ + 163.83
(25)(0.9) = (Fg + Fy) * μ + 163.83
and I end up with Ffr = 141.33N [backwards], and the coefficient of friction ends up to be 0.393.

To find the force required to keep the lawnmower in constant velocity: (Letting x2 and y2 be the new components of the second applied force)
Ffr2 = Fx2
FN2 + Fy2 * μ = (245 + Fy2) * 0.393 = Fx2

I tried my best to show and explain what I have so far, but I don't know how to continue. I only have 1 equation and 2 unknowns. (The answer to the question is apparently 168N)

EDIT:
I noticed a second relation that can be used: Fx2 * tan35 = Fy2
But when I solve the 2 unknowns using the 2 equations, I end up with;
Fx2 = 132.840N [forward]
Fy2 = 92.992N [down]
And if I use the Pythagorean theorem, I end up with Fapp2 = 162N [35degrees below horizon], which is a little different than the answer of 168N.

Last edited:

Thank you for your post and for showing your work. Your approach is on the right track, but there are a few things that need to be corrected in order to get the correct answer of 168N.

First, when finding the components of the 200N force, you should use the sine and cosine functions with respect to the horizontal, not the vertical. This is because the angle given is measured from the horizontal, not the vertical. So the equations should be:

Fx = 200cos35 = 163.83N [forward]
Fy = 200sin35 = 114.71N [up]

Next, when setting up the equations for the net force, you should use the friction force as the unknown, not the net force. This is because the friction force is the force that is opposing the applied force and causing the acceleration. So the equations should be:

Ffr = ma - Fx
Ffr = μFN

Substituting in the values, we get:

Ffr = (25)(0.9) - 163.83
Ffr = 141.33N [backwards]

μFN = (25)(9.8)(0.393)
μFN = 96.135N

Now, to find the force required to maintain constant velocity, we can use the same equations, but with the acceleration set to 0 since the mower is not accelerating. So we get:

Ffr2 = Fx2
Ffr2 = μFN2

Substituting in the values, we get:

Ffr2 = 163.83 - Fx2
μFN2 = 96.135N

Solving for Fx2, we get:

Fx2 = 163.83 - 96.135 = 67.695N [forward]

Finally, to find the total force required to maintain constant velocity, we can use the Pythagorean theorem to find the magnitude of the force:

Fapp2 = √(Fx2^2 + Fy2^2)
Fapp2 = √(67.695^2 + 114.71^2)
Fapp2 = 168N

I hope this helps clarify your approach and leads you to the correct answer. Keep up the good work!

## What is Newton's Law?

Newton's Law is a fundamental principle in physics that states that an object will remain at rest or in motion at a constant velocity unless acted upon by an external force.

## How does angled applied force affect an object's motion?

When a force is applied at an angle to an object, it can be broken down into two components: one parallel to the object's motion and one perpendicular to it. The parallel component will cause the object to accelerate in the direction of the applied force, while the perpendicular component will cause the object to change direction.

## What is friction and how does it affect an object's motion?

Friction is a force that opposes motion between two surfaces that are in contact. It is caused by the microscopic roughness of the surfaces and can slow down or stop an object's motion.

## How does the angle of an applied force affect friction?

The angle of an applied force can affect the amount of friction between two surfaces. When the force is applied at an angle, the perpendicular component of the force will increase the normal force between the surfaces, which in turn increases the friction force. This means that the greater the angle of the applied force, the greater the friction force will be.

## What is the relationship between applied force and friction?

The relationship between applied force and friction can be described by the equation Ff = μFn, where Ff is the friction force, μ is the coefficient of friction, and Fn is the normal force. This means that the greater the applied force, the greater the friction force will be, but it also depends on the coefficient of friction and the normal force between the surfaces.

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