Finding the normal force from a lawnmower pushed at 32 degrees

[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??!?

 

[p3mulis]

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!

 

[lolzwhut?]

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 :)