# Finding Time with Work and Distance

• vuhwhat
In summary, the problem setter wants the student to calculate the net work done by the lawnmower on a given area of lawn using the F=ma equation and the assumption that the lawnmower starts from rest.
vuhwhat
Homework Statement
A person pulls on a 20kg lawnmower with a force of 25.0N and moves the mower 4.50metes. The handle angle is 15* with the horizontal and μ=0.100.

What I've found:

a) Work done by person = 109J
B) Work done by friction= -85.3J
C) Find the time= ?
Relevant Equations
P=W/T
W= Fd
I tried using the 109 J to convert to seconds but that didn't work. I also looked through the energy equations but nothing worked. I am not sure how to find time.

Delta2
Can you relate the total work done to the final velocity of the mower?

The time is related to the distance traveled and the average velocity.

Or you can find the acceleration from the net horizontal force and use the kinematic equation relating acceleration, distance and time. It is appropriate to assume that the lawnmower starts from rest.

Delta2
TSny said:
Can you relate the total work done to the final velocity of the mower?

The time is related to the distance traveled and the average velocity.
F=ma --> a=F/m...
a= 25N/20kg
a= 1.25 m/s^2..

Acceleration is the change in speed so a=vt.. But I'm not sure how I find velocity?

I think you got to take into account the force of friction as well, in order to calculate the net acceleration.

Once you find the net acceleration ##a##, use the equation ##s=v_0t+\frac{1}{2}at^2## to find the time. We assume that the lawnmower starts from rest, that is ##v_0=0##, I am not sure if this is a perfectly safe assumption though.

Last edited:
Delta2 said:
you got to take into account the force of friction
and the angle at which the tractive force is applied. And don't forget to calculate the normal force correctly.

malawi_glenn and Delta2
haruspex said:
and the angle at which the tractive force is applied. And don't forget to calculate the normal force correctly.
Oh damn how could I forget all this...Yes especially the normal force which won't be equal to the weight...

The problem setter apparently intends that the tractive force is applied along the axis of the handle, though most mowers are equipped with stops that prevent handle travel beyond a certain range and thus permit forces with other directions as well.

Delta2
OP has correctly calculated the works in parts (a) and (b) which cannot be done without the correct expression of the normal force. The connection that OP missed is that, in this case,
$$W_{\text{net}}=W_{\text{F}}+W_{\text{fr.}}=F_{\text{net,x}}~\Delta x=m~a~\Delta x~\implies~a =\frac{W_{\text{F}}+W_{\text{fr.}}}{m\Delta x}.$$

Delta2

## 1. How do I calculate time with work and distance?

To calculate time with work and distance, you can use the formula: time = distance / work. This formula is based on the concept that time is equal to the distance traveled divided by the speed at which the distance is covered, also known as work. This formula is commonly used in physics and can be applied to various scenarios, such as calculating travel time or solving for time in a work rate problem.

## 2. What is the relationship between work, distance, and time?

Work, distance, and time are all interconnected in the formula: work = force x distance. This formula is derived from the concept of work being equal to the force applied to an object multiplied by the distance the object moves. In terms of finding time with work and distance, the formula can be rearranged to solve for time as mentioned in the previous answer.

## 3. Can you provide an example of finding time with work and distance?

Sure! Let's say you are planning a road trip and need to calculate how long it will take you to reach your destination. The distance between your starting point and destination is 500 miles, and you plan to drive at a constant speed of 60 miles per hour. Using the formula time = distance / work, we can plug in the values to get time = 500 miles / 60 miles per hour. This gives us a total travel time of 8.33 hours or approximately 8 hours and 20 minutes.

## 4. How does speed affect the time with work and distance?

Speed plays a crucial role in the calculation of time with work and distance. The higher the speed, the shorter the time it takes to cover a certain distance. This is because speed is directly proportional to distance and inversely proportional to time. In other words, the faster you travel, the more distance you cover in a shorter amount of time.

## 5. Is there a difference between calculating time with work and distance for different modes of transportation?

Yes, the formula for calculating time with work and distance may vary depending on the mode of transportation. For example, if you are traveling by plane, you would need to consider factors such as airspeed and wind resistance in your calculations. Similarly, if you are traveling by boat, you would need to factor in the speed of the current and water resistance. However, the basic concept of time being equal to distance divided by work remains the same for all modes of transportation.

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