# Solve Work & KE Problems with Expert Help

In summary: The area under the line is the work done.In summary, the conversation discusses different methods to solve for the work done in a problem involving kinetic energy and a non-constant force. The first method involves using the work energy theorem and solving for velocity, but this method is not accurate. The second method involves using an integral to approximate the work done over a certain distance, but the conversation suggests using the simpler method of finding the area under the line. This method is more accurate and involves basic graphical integration.

Well, according to the rules you're supposed to show your efforts to solve this. Since you didn't do that, I assume you don't have any to show. I'll get you started:

(1) We'll assume friction is being ignored. Then the work done goes into generating kinetic energy.

(2) Work done is given by

$$W = \int \mathbf{F} \cdot d \mathbf{l}$$

(3) Since the force is not constant you need the equation for the force.

That should get you started.

oops i forgot that xD

I tried to solve this using a work energy theorem
W=KEfinal-KEinitial

SO because it is starting at rest the KE initial is zero

THerefore the equation would be W =.5mv^2

When solving for v, I get like 10.59, not an answer near the possible ones

Also we haven't learned integrals or whatever that L is in the equation you gave me, is there an easier way to start off?

Also we haven't learned integrals or whatever that L is in the equation you gave me, is there an easier way to start off?

Well, there is. You can approximate the integral in the following way: Break the horizontal distance from 0 to 150 up into convenient length segments, for starters, say 15 meters wide. That will give you 10 segments. From the graph estimate the average force over that segment (I'd pick the midpoint of the segment). Multiply that value by 15 meters. That gives you a
$$\Delta W$$ for that segment. Do this 10 times, once for each segment and add them up. That's an approximation to the total work. Set that equal to the kinetic energy and solve for v.

(1) The more segments you take the better the approximation.

(2) I just thought of this --you can take the midpoint of your segment and substitute it into the equation of the line to get an approximate average force for that segment

(3) What you are doing here is a simple graphical integration. Keep it in mind when you study calculus

Could I just find the area under the line?

Awesome, I used an intergral function on my calculator to find its total work, then set that to v. Thanks a ton!

Could I just find the area under the line?

Well, duh. Why didn't I think of that?

Answer --I was too wrapped up in the line integral idea.

## 1. How can I solve work and kinetic energy problems?

To solve work and kinetic energy problems, you can use the following equations:
- Work (W) = Force (F) x Displacement (d)
- Kinetic Energy (KE) = 1/2 x Mass (m) x Velocity (v)^2
You can also use the principle of conservation of energy, which states that the total energy in a closed system remains constant.

## 2. What are some common types of work and kinetic energy problems?

Some common types of work and kinetic energy problems include finding the work done on an object, the kinetic energy of an object, and the speed or mass of an object given its kinetic energy.

## 3. Can I get expert help with solving work and kinetic energy problems?

Yes, there are many resources available for getting expert help with solving work and kinetic energy problems. You can consult with a physics tutor, join a study group, or use online resources such as videos and practice problems.

## 4. How do I approach solving a work and kinetic energy problem?

To solve a work and kinetic energy problem, it is important to first identify the given variables and what you are trying to find. Then, use the appropriate equations and principles to solve for the unknown variable. It can also be helpful to draw a diagram and label all the given information.

## 5. What are some common mistakes to avoid when solving work and kinetic energy problems?

Some common mistakes to avoid when solving work and kinetic energy problems include using the wrong equations, not considering all the relevant forces and energies involved, and not properly converting units. It is also important to double-check your calculations and make sure they make sense in the context of the problem.

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