Question

"The x component of the force on an object varies as shown in Fig. 6-36.

Figure 6-36
(a) Determine the work done by this force to move the object from x = 0.0 to x = 3.0 m.


J
(b) Determine the work done by this force to move the object from x = 0.0 to x = 10.0 m.
J"

Answer 1

The work done by a force with varying x-component can be calculated by integrating the force function with respect to x. In this case, the force function is given by Fx = -kx. We can plug in the values for x and integrate the expression to find the work done.

Step-by-step explanation:

To calculate the work done by a force with varying x-component, we need to integrate the force function with respect to x from the initial position to the final position. In this case, the force function is given by Fx = -kx. We can plug in the values for x and integrate the expression to find the work done.

(a) For x = 0.0 to x = 3.0 m:

W = ∫(-kx)dx = ∫(-kx)dx = -k∫xdx = -k[x^2/2]

Substituting the values, we get:

W = -k[(3^2/2) - (0^2/2)] = -k(9/2)

(b) For x = 0.0 to x = 10.0 m:

W = ∫(-kx)dx = ∫(-kx)dx = -k∫xdx = -k[x^2/2]

Substituting the values, we get:

W = -k[(10^2/2) - (0^2/2)] = -k(100/2)

Answer 2

a) 2,800Joules

b)600 Joules

Step-by-step explanation:

a) we're basically looking at a force x position graph. And we may know already that work = the force x the displacement, but since this only works if the force is constant (when this happens it looks like a straight line making a square/rectangular graph with respect to position in m) So, in order to do this with varying force, you take the area of the inside shape made by the graph! This is going to give you the value for the work done. From x=0 to x= 10 it looks we have a nice old traoezoid. The area of a trapezoid is A=(a+b)/2 *h. a being the top of the trapezoid, b being the base of the trapezoid, and h being the height of the trapezoid.

A= (4 +10)/2 *400

A= 2,800 Joules

b) same thing, find the area. This time its a triangle so the Area= 1/2 b*h

So, it ends up being 1/2(3*400)

A=600 Joules