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(solution) Consider the force field set up by wind on the surface of a


Consider the force field set up by wind on the surface of a partially treed park. The force

field for the surface of the park is illustrated in Figure 2. This figure shows no force in the

treed area, where there is no wind, and a non-zero force in an open area, where there is wind.

Assume the wind in the open area exerts a force on a person proportional to the mass of the

person with constant ___ N/kg. (The only objects of interest are people on foot). The treed

area is such that people can walk through it. Points A, B, C and D mark the corners of a

100 m by 120 m rectangle. A to B = C to D = 120 m, B to C = D to A = 100 m.


Figure 2: Non-Conservative Force Field where force is either zero or ___ N/kg


(a) Prove that this is a non-conservative force field. (In a conservative force field, zero net

energy is required to move an object along any path that ends where it started.)

(b) Show that the concept of constant energy contours does not exist in a non-conservative

force field. This can be done by first showing that the energy of an object is not changed

if it is moved along A-B-C-D in Figure 2, which means points A and D must be at the

same energy levels. Then show that this is not the case (i.e. the energy does change) if

the object is moved in a straight line from point A to D.


Consider the force field set up by wind on the surface of a partially treed park. The force

 

field for the surface of the park is illustrated in Figure 2. This figure shows no force in the

 

treed area, where there is no wind, and a non-zero force in an open area, where there is wind.

 

Assume the wind in the open area exerts a force on a person proportional to the mass of the

 

person with constant ___ N/kg. (The only objects of interest are people on foot). The treed

 

area is such that people can walk through it. Points A, B, C and D mark the corners of a

 

100 m by 120 m rectangle. A to B = C to D = 120 m, B to C = D to A = 100 m. Figure 2: Non-Conservative Force Field where force is either zero or ___ N/kg (a) Prove that this is a non-conservative force field. (In a conservative force field, zero net

 

energy is required to move an object along any path that ends where it started.)

 

(b) Show that the concept of constant energy contours does not exist in a non-conservative

 

force field. This can be done by first showing that the energy of an object is not changed

 

if it is moved along A-B-C-D in Figure 2, which means points A and D must be at the

 

same energy levels. Then show that this is not the case (i.e. the energy does change) if

 

the object is moved in a straight line from point A to D.

 


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