# Solving a Puzzling Homework Problem: Pushing a Lawn Mower

• iRaid
In summary, the conversation discusses a problem involving a person pushing a lawn mower with a force of 88.0N at an angle of 45.0(degrees) to the horizontal. The person must find the horizontal friction force, the normal force exerted by the ground, and the force needed to accelerate the lawn mower from rest to 1.5 m/s in 2.5 seconds. The solution involves using the equations Fx = F cos (theta), Fy = F sin (theta), F = ma, and a = (vf-vi)/t. The final answer for the normal force is 199.43 N.
iRaid

## Homework Statement

Well I don't think my teacher explained this very well so I need some help.. Thank you in advance.

26.) 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 at an angle of 45.0(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

Fx = F cos (theta)
Fy = F sin (theta)
F = ma
a = (vf-vi)/t

## The Attempt at a Solution

b) Fx = 88 cos 45 = 62.2N

c) I thought it would be the vertical component, but it's not, not sure where to go from that now..

d) Not sure :(

Thanks.

Im pretty sure your Fp should be pointing in the third quadrant, you don't push up on a lawn mower. To find the Normal just sum the forces in the Y direction and solve for Fn

Last edited:
The answer is 199 though :|

yes the answer is 199.43 N, you need to correct your diagram

[PLAIN]http://img836.imageshack.us/img836/3172/blockl.png

Now sum the forces in the Y direction

Forces in Y = Fn - Fg - Fpsin(t) = 0;

Last edited by a moderator:

I would first like to commend you for seeking help and clarification on this homework problem. It is important to fully understand the concepts and equations involved in order to accurately solve the problem.

To start, let's draw a free-body diagram for the lawn mower. This will help us visualize all the forces acting on the mower.

In this case, we have the applied force of 88N at an angle of 45 degrees, the weight of the lawn mower (mg), the normal force from the ground (N), and the friction force (Ffr) acting in the opposite direction of motion.

Using the equations Fx = F cos(theta) and Fy = F sin(theta), we can determine the horizontal and vertical components of the applied force.

Fx = 88 cos 45 = 62.2N
Fy = 88 sin 45 = 62.2N

Now, for part b, we can use Newton's second law (F=ma) to solve for the friction force. Since we know the mass of the lawn mower (14.0kg) and the acceleration is zero (since it is moving at a constant speed), we can rearrange the equation to solve for the friction force.

F = ma
62.2N = (14.0kg)(0)
Ffr = 0N

This means that the friction force on the lawn mower is zero since it is moving at a constant speed.

Moving on to part c, we can use Newton's third law (for every action there is an equal and opposite reaction) to determine the normal force exerted by the ground on the lawn mower. In this case, the normal force is equal in magnitude to the weight of the lawn mower (mg).

N = mg
N = (14.0kg)(9.8m/s^2)
N = 137.2N

For part d, we can use the equation a = (vf-vi)/t to solve for the acceleration of the lawn mower. We know the final velocity (vf) is 1.5m/s, the initial velocity (vi) is 0m/s, and the time (t) is 2.5 seconds.

a = (1.5m/s - 0m/s)/2.5s
a = 0.6m/s^2

Now, using F=ma, we can solve for the force needed to accelerate

## 1. How do I start solving a puzzling homework problem about pushing a lawn mower?

To start solving this problem, you should first carefully read and understand the given instructions and any relevant formulas or equations. It may also be helpful to draw a diagram or make a list of the given information.

## 2. What are the key factors to consider when solving this problem?

The key factors to consider in pushing a lawn mower include the force applied, the angle and direction of the force, the weight of the lawn mower, and the friction between the lawn mower and the ground.

## 3. How can I determine the amount of force needed to push the lawn mower?

You can determine the amount of force needed by using the formula F = ma, where F is force, m is mass, and a is acceleration. You will need to know the mass of the lawn mower and the desired acceleration.

## 4. What role does friction play in pushing a lawn mower?

Friction plays a major role in pushing a lawn mower, as it is the force that opposes the motion of the lawn mower. The amount of friction will depend on the weight of the lawn mower, the surface of the ground, and any other external factors.

## 5. Are there any tips for solving this problem more efficiently?

One tip for solving this problem more efficiently is to break it down into smaller, more manageable parts. You can also use trial and error to find the right combination of force and angle to successfully push the lawn mower. Additionally, double-check your calculations and make sure to include all relevant factors in your solution.

Replies
2
Views
2K
Replies
4
Views
1K
Replies
6
Views
5K
Replies
18
Views
12K
Replies
4
Views
21K
Replies
4
Views
4K
Replies
6
Views
6K
Replies
2
Views
5K
Replies
2
Views
3K
Replies
2
Views
4K