Speed with work energy theorem

In summary, the conversation discusses the possibility of using Newton's second law and constant acceleration kinematics equations to check for a 50m variable force problem. It is determined that these equations cannot be used because the force is not constant. However, it is possible to check the problem analytically by using kinematics equations that account for variable acceleration.
  • #1
PAstudent
47
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1. Homework Statement

The Attempt at a Solution



I was wondering if I did something wrong for the 50m. I did the same process of finding the area under the line. I'm assuming it's possible to get the same speed since the net work is the same.[/B]
 
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  • #2
Yes, it will be the same as for 20.
 
  • #3
The 50m cannot be checked because it has a variable force from 20-50 and no longer a constant acceleration
 
  • #4
PAstudent said:
The 50m cannot be checked because it has a variable force from 20-50 and no longer a constant acceleration
Not sure what you mean. Do you mean it cannot be checked analytically? It can. You would need to express the variable force as a function of x and integrate with respect to x to find the work done.
 
  • #5
It says explain why Newton's second law and the constant acceleration kinematics equations cannot be used to check for the 50m
 
  • #6
PAstudent said:
It says explain why Newton's second law and the constant acceleration kinematics equations cannot be used to check for the 50m
Yes, but that says using "constant acceleration" kinematics. As you say, it is not constant acceleration. But it can be checked analytically by using kinematics that cope with variable acceleration because the nature of that variation is known exactly.
 

1. What is the work-energy theorem?

The work-energy theorem states that the work done on an object is equal to the change in its kinetic energy. This means that when a force acts on an object to move it, the energy transferred is equal to the change in its motion.

2. How is speed related to the work-energy theorem?

According to the work-energy theorem, the work done on an object is equal to the change in its kinetic energy. This means that if the work done on an object increases, its kinetic energy will also increase, resulting in an increase in speed.

3. Can the work-energy theorem be applied to all types of motion?

Yes, the work-energy theorem can be applied to all types of motion, whether it is linear, rotational, or a combination of both. As long as there is a force acting on an object and causing a change in its motion, the work-energy theorem can be used to analyze the situation.

4. What is the formula for calculating work using the work-energy theorem?

The formula for calculating work using the work-energy theorem is W = ΔK = 0.5mv2f - 0.5mv2i, where W is work, ΔK is the change in kinetic energy, m is the mass of the object, vf is the final velocity, and vi is the initial velocity.

5. Can the work-energy theorem be used to calculate the speed of an object?

Yes, the work-energy theorem can be used to calculate the speed of an object if the mass and initial and final velocities are known. By rearranging the formula, vf = √(2W/m + vi2), the final speed of the object can be determined.

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