How Do You Calculate Work Done on a Particle Given Its Position-Time Equation?

In summary, the conversation involves finding the work done on a 3.6 kg object by a single force using the equation x = 4.1t - 0.64t2 + 2.0t3. The concept of finding the work done using the integral of Fx is mentioned, along with the question of how to find Fx. There is also discussion about what else can be determined from the given information, such as the motion and displacement of the object.
  • #1
phyphyphy
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I was given the problem:

A single force acts on a 3.6 kg particle-like object in such a way that the position of the object as a function of time is given by x = 4.1t - 0.64t2 + 2.0t3, with x in meters and t in seconds. Find the work done on the object by the force from t = 0 to t = 8.1 s.

I know that W= integral of Fx, but how do I find Fx?
 
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  • #2
If ##x(t) = 4.1t - 0.64t^2 + 2.0t^3##, what else can you find about the motion, as well as the displacement?

I know that W= integral of Fx
That's one way to solve the problem, but what else is W equal to?
 

1. What is the definition of force?

Force is a physical quantity that can change the state of motion or shape of an object. It is measured in Newtons (N) and is represented by the symbol F.

2. How is force related to work?

Force and work are directly related. Work is the product of force and the displacement in the direction of the force. This can be expressed as W = F x d, where W is work, F is force, and d is displacement.

3. Can you explain the difference between work and power?

While work is the amount of energy required to move an object, power is the rate at which work is done. It is measured in Watts (W) and is represented by the symbol P. Power is equal to work divided by time, or P = W/t.

4. How does the angle between force and displacement affect work?

The angle between force and displacement affects the amount of work done. When the force and displacement are in the same direction, all of the force is used to do work. However, when the force and displacement are perpendicular, no work is done.

5. How can we calculate the work done by a variable force?

To calculate the work done by a variable force, we can use integration. This involves breaking the force into small intervals and calculating the work done in each interval. The total work done is then found by adding up the work done in each interval.

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