A object of mass 3.00 kg is subject to a force Fx that varies with position as in the figure below.
Find the work done by the force on the object as it moves as follows:
(a) from x = 0 to x = 4.00 m
1
Your response differs from the correct answer by 10% to 100%. J
(b) from x = 5.00 m to x = 7.00 m
2 J
(c) from x = 14.0 m to x = 15.0 m.
3 J
(d) If the object has a speed of 0.500 m/s at x = 0, find its speed at x = 5.00 m and its speed at x = 15.0 m. speed at x = 5.00 m 4 m/s
speed at x = 15.0 m 5 m/s
To find the work done by a force on an object, we can use the formula:
Work = Force * Distance * cos(theta)
In this case, we are given the force Fx as a function of position. To find the work, we need to integrate the force over the given distance.
(a) From x = 0 to x = 4.00 m:
To find the work done over this distance, we need to calculate the integral of the force function from x = 0 to x = 4.00 m.
Work = ∫(0 to 4) Fx(x) dx
Using the given figure or description, we can determine the expression for Fx(x) and then evaluate the integral to find the work done.
(b) From x = 5.00 m to x = 7.00 m:
Again, we need to integrate the force function over the given distance.
Work = ∫(5 to 7) Fx(x) dx
(c) From x = 14.0 m to x = 15.0 m:
Once again, we need to integrate the force function over the given distance.
Work = ∫(14 to 15) Fx(x) dx
(d) To find the speed of the object at x = 5.00 m and x = 15.0 m, we can use the work-energy theorem. The work done on an object is equal to the change in its kinetic energy.
Work = ΔKE
Since the object starts with a speed of 0.500 m/s at x = 0, we can set the initial kinetic energy to zero. Then we can equate the work done to the change in kinetic energy to find the final speed.
Work = KE_final - KE_initial
To find the speed at x = 5.00 m:
Work from x = 0 to x = 5.00 m = KE_final - 0
Using the previously calculated work, we can determine the final kinetic energy and subsequently the speed.
To find the speed at x = 15.0 m:
Work from x = 0 to x = 15.0 m = KE_final - 0
Using the previously calculated work, we can determine the final kinetic energy and subsequently the speed.
a. 5
b. ?
c. 3
d. ?/?