How Do Newton's Laws Apply to Pushing a Lawn Mower?

In summary, a person is pushing a lawn mower with a force of 88.0N at a 45 degree angle to the horizontal. The horizontal friction force is 62N and the normal force exerted by the ground is 199.425N. The force required to accelerate the lawn mower from rest to 1.5 m/s in 2.5 seconds is 0.6 m/s^2. The equation x-x_0=v_0 t+1/2 at^2 can be used to derive the average velocity of a car and the speed of a follower gear.
  • #1
seizureboi
8
0

Homework Statement



A person pushes a 14.0-kg lawn mower at constant speed with a force of F= 88.0N directed along the handle, which is set at an angle of 45 degrees to the horizontal. (a) Draw the free-body diagram showing all forces acting on the mower. Calculate (b) the horizontal friction force on the mower, then (c) the normal force exerted vertically upward on the mower by the ground. (d) What force must the person exert on the lawn mower to accelerate it from rest to 1.5 m/s in 2.5 seconds, assuming the same friction force?

Homework Equations


m = 14 kg
g = 9.8 m/s2
t = 2.5 seconds
F = ma
NF= mg
v = v0 + at

The Attempt at a Solution



(a) I did the free-body...simple

(b) 88cos(45)-friction force=ma a=0 therefore, 88cos(45)=horizontal friction force= 62N

(c) NF= mg+88sin(45) --> NF= (14)(9.8)+88sin(45)=199.425N

(d) I used the last equation that I put down and i got the acceleration to be .6 m/s2 and I don't know what to do afterwards.

I just think that I'm wrong in every single one...except the free-body =)
 
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  • #2
d, F = m a
You have the 'a' you just need the 'f'
 
  • #3
A car having a mass of 1127 kg is traveling on a level road with a uniform velocity. The horizontal force required to obtain an acceleration of 5 m per sec per sec is?
 
  • #4
If the driver of a pair of gear contains 80 teeth and has a speed of 120 rpm, the speed of the follower gear with 64 teeth is?
 
  • #5
Don't forget the good old

x-x_0=v_0 t+1/2 at^2

... and how to derive it;

x-x_0:distance

average velocity=(v_0+v)/2
average velocity=(x-x_0)/t

(v_0+v)/2=(x-x_0)/t
t(v_0+v)=2(x-x_0)
{v=v_0+at}
x-x_0=1/2 (v_0+v)t
x-x_0=1/2 v_0 t+1/2 vt
x-x_0=1/2 v_0 t+1/2 (v_0+at)t
x-x_0=1/2 v_0 t+1/2 v_0 t+1/2 at^2

x-x_0=v_0 t+1/2 at^2
 

FAQ: How Do Newton's Laws Apply to Pushing a Lawn Mower?

1. What are Newton's Laws and how do they relate to a lawn mower?

Newton's Laws are three fundamental principles in physics that explain the relationship between an object's motion and the forces acting upon it. They apply to all objects, including lawn mowers, and help us understand how they move and why they stop.

2. How does the first law of motion apply to a lawn mower?

The first law, also known as the law of inertia, states that an object at rest will stay at rest and an object in motion will stay in motion at a constant velocity unless acted upon by an external force. This means that a lawn mower will not start moving on its own, but once it is pushed or pulled, it will continue to move until a force, such as friction or the ground, stops it.

3. What is the significance of the second law of motion when it comes to a lawn mower?

The second law, also known as the law of acceleration, states that the acceleration of an object is directly proportional to the net force acting upon it and inversely proportional to its mass. In the case of a lawn mower, this means that the harder you push or pull it, the faster it will accelerate, and the heavier the lawn mower is, the more force it will take to move it.

4. How does the third law of motion apply to a lawn mower?

The third law, also known as the law of action and reaction, states that for every action, there is an equal and opposite reaction. In terms of a lawn mower, this means that when the blades rotate and cut through the grass, the grass exerts an equal and opposite force on the blades, helping to propel the lawn mower forward.

5. Can Newton's Laws help me improve my lawn mowing technique?

Yes, understanding these laws can help you mow your lawn more efficiently. For example, knowing the second law can help you determine the optimal amount of force to use when pushing or pulling the lawn mower, and the third law can remind you to keep the blades sharp to reduce the amount of force needed to cut through the grass.

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