Work done by a general force

In summary, the conversation discusses the calculation of the kinetic energy of a 1.5 kg block on a horizontal frictionless surface, using a given horizontal force function. The question is posed whether the answers for the kinetic energy at x = 2.0 m and the maximum kinetic energy between x = 0 and x = 2.0 m would be the same. The answer is that they would not be the same, as the force changes direction at some point between these two positions. The calculation is performed by integrating the force function from the initial position to the final position, giving a result of 2 1/3 J for both a and b.
  • #1

missrikku

Hello again! I just want to check if this is correct..

A 1.5 kg block is initially at rest on a horizontal frictionless surface when a horizontal force in the pos direction of an x-axis is applied to the block. The force is given by F(x) = (2.5 - x^2)i N, where x is in m and the initial position of the block is x = 0.

a) what is the kinetic energy of the block as it passes through x = 2.0 m?

b) what is the maximum kinetic energy of the block between x = 0 and x = 2.0 m


Wouldn't I get the same answer for both a and b?

I did the following:

** S = integral sign

W = S F(x)dx = Kf - Ki

with xi = 0 and xf = 2.0:

S F(x)dx = 2.5x -x^3/3 --> 2 1/3 J

Wouldn't the ans for both a and be be 2 1/3 J?

Thanks!
 
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  • #2
Yes, since this is a horizontal surface, there is no change in potential energy so the change in kinetic energy must be the work done by the force. Integrating the force form the initial point to the last gives that work.

"Wouldn't the ans for both a and be be 2 1/3 J?"

Would it? Certainly the speed and energy will be increasing as long as the force is in the same direction but they will start decreasing when the force changes direction. Where does the force change direction?
 
  • #3


Your approach is correct and you have correctly calculated the work done by the force F(x) on the block as it moves from x = 0 to x = 2.0 m. However, the work done by a force is not equal to the kinetic energy of the object. Kinetic energy is the energy possessed by an object due to its motion, and it is equal to 1/2 mv^2, where m is the mass of the object and v is its velocity.

To find the kinetic energy of the block at x = 2.0 m, you need to use the work-energy theorem, which states that the work done by a force is equal to the change in kinetic energy of the object. In this case, the work done by the force F(x) will result in a change in the kinetic energy of the block from its initial value (which is zero, since it is initially at rest) to its final value at x = 2.0 m.

So, to answer part (a), you need to calculate the work done by the force F(x) from x = 0 to x = 2.0 m, and then use this value to find the change in kinetic energy of the block. This will give you the kinetic energy of the block at x = 2.0 m.

To answer part (b), you need to calculate the maximum kinetic energy of the block between x = 0 and x = 2.0 m. This will be the maximum value of kinetic energy that the block reaches during its motion, and it will occur at a specific point between x = 0 and x = 2.0 m. To find this point, you can use the fact that the work done by a force is maximum when the force is parallel to the displacement of the object. So, you need to find the point at which the force F(x) is parallel to the displacement of the block, and then calculate the work done by this force at that point. This will give you the maximum kinetic energy of the block between x = 0 and x = 2.0 m.

Therefore, the answers to parts (a) and (b) will be different, as they are asking for two different things - the kinetic energy of the block at a specific point, and the maximum kinetic energy reached during its motion. I hope this helps clarify your understanding of work and kinetic energy. Keep up the good
 

What is work done by a general force?

Work done by a general force is a measure of the energy transferred to an object by a force, resulting in a displacement of the object in the direction of the force.

How is work calculated?

Work is calculated by multiplying the magnitude of the force by the displacement of the object in the direction of the force. This can be represented by the equation W = F * d, where W is work, F is force, and d is displacement.

Can work be negative?

Yes, work can be negative. This occurs when the force and displacement are in opposite directions, resulting in the force doing negative work on the object.

What are the units of work?

The units of work are joules (J) in the International System of Units (SI). In other systems, work may be measured in foot-pounds (ft-lb) or ergs (erg).

How is work related to energy?

Work and energy are closely related concepts, with work being a measure of the energy transferred to an object. The unit of work, joules, is also the unit of energy. This means that when work is done on an object, its energy increases. Similarly, when work is done by an object, its energy decreases.

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