# Magnitude of vertical force. What am I doing wrong? x_X

• lolzwhut?
In summary, the woman is pushing a 20 kg lawnmower at a steady speed with a force of 87 N at an angle of 32 degrees below the horizontal. The acceleration of gravity is 9.8 m/s^2. To find the magnitude of the vertical force the lawnmower exerts on the lawn, we can use the formula F=ma and the trigonometric function sin(x) to determine the vertical component of the force. By adding the weight of the lawnmower (mg) and the vertical component of the force of the push (87sin(32)), we get a total magnitude of 242.1 N.
lolzwhut?

## Homework Statement

A woman pushes a 20 kg lawnmower at a steady speed. She exerts a 87 N force in a direction of 32 (degrees) below the horizontal. The acceleration of gravity is 9.8 m/s^2. Find the magnitude of the vertical force this lawnmower exerts on the lawn. Answer in units of N.
• So, mass of lawn mower is 20 kg.
• She exerts a 87 N force.
• Force is exerted at 32 degrees.
• Acceleration of gravity is 9.8 m/s^2.
• ?magnitude of the vertical force this lawnmower exerts on this lawn?

## Homework Equations

• F=ma
• Trigonometric: sin(x)

## The Attempt at a Solution

I first wanted to show you a picture of the problem:

http://img10.imageshack.us/img10/8034/lawnmowerproblm.jpg

So what I did:

|\
|..\
|...\ 87N
|x...\
|...\
|___x_32\

So I did Sin(32) = x/87
Sin(32)*87 = x
X = 46.103, thus which I thought was the downward force exerted.
Unfortunately it's not.

What am i doing wrong??!?

Last edited by a moderator:
I think if you are finding the force the lawnmower is exerting on the ground just take mg and add it to the vertical component of the force of the push.

So mg = (20kg)*(9.8)=196N
And the vertical component of the force is 87sin(32)=46.1N

Then just add them together because they are both pointed downward. First post!

p3mulis said:
I think if you are finding the force the lawnmower is exerting on the ground just take mg and add it to the vertical component of the force of the push.

So mg = (20kg)*(9.8)=196N
And the vertical component of the force is 87sin(32)=46.1N

Then just add them together because they are both pointed downward.

First post!

Ah ha! That's what I forgot to do! I forgot to do (20kg)*(9.8)=196N Thanks man! That's exactly right :)

## 1. What is the magnitude of vertical force?

The magnitude of vertical force is the amount of force exerted in the vertical direction, either upwards or downwards.

## 2. How is the magnitude of vertical force measured?

The magnitude of vertical force is typically measured in units of Newtons (N) using a force sensor or a spring scale.

## 3. What factors affect the magnitude of vertical force?

The magnitude of vertical force is affected by the mass of an object, the acceleration due to gravity, and any additional forces acting in the vertical direction (such as friction or air resistance).

## 4. What is considered a "normal" or "average" magnitude of vertical force?

The normal or average magnitude of vertical force can vary greatly depending on the situation. For example, a person standing on the ground may exert a vertical force of approximately their body weight, while a rocket taking off may exert a vertical force thousands of times greater than its weight.

## 5. What could I be doing wrong if I am getting a negative magnitude of vertical force?

A negative magnitude of vertical force typically means that the force is acting in the opposite direction than what was expected. Double check the direction of your force measurement and any other forces acting on the object to determine the correct sign of the force.

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