How much work is required to push a chair across the floor with a force of F=8lbF=8\operatorname{lb} from x=6ftx=6\operatorname{ft} to x=9ftx=9\operatorname{ft} along the xx-axis?

24 ft ⁡ ⋅ lb ⁡ s 24\operatorname{ft}\cdot\operatorname{lb}s

How much work is required to push a chair across the floor with a force of F = 8 lb F=8\operatorname{lb} from x = 6 ft x=6\operatorname{ft} to x = 9 ft x=9\operatorname{ft} along the x x -axis?

this problem, we're asked how much work is required to push a chair across the floor with a force of eight pounds from x equals six feet to x equals nine feet along the x axis. So this is the work problem we're dealing with, and notice that we have a constant force in this problem. This is not some function, like a function of x here, this is just a force of eight pounds. So what that means, we can use this equation. The work is going to be equal to force times distance, right here. So if I wanna go ahead and calculate this, well, our force, I can see is eight pounds. We have eight pounds. And our distance, I can see, goes from six feet to nine feet. Now what exactly would this distance be here? Well, what we ultimately need to do is figure out what our distance is from six feet all the way over to nine feet. So what I can do is I can take my nine feet and then I can subtract off my six feet. Because notice how I'd be finding this difference between the two right here. So this is what I can do, and then six feet minus nine feet is three feet. So we have eight pounds minus three feet, and eight times three is 24. So we're gonna have 24 in our units. Well, we have feet and pounds, so our unit is going to be in foot pounds. And this right here would be the work required to move this chair across the floor. So that is how you can calculate these work problems and find your solution. Hope you found this video helpful, and let's move on.

How much work is required to push a chair across the floor with a force of F = 8 lb ⁡ F=8\operatorname{lb} from x = 6 ft ⁡ x=6\operatorname{ft} to x = 9 ft ⁡ x=9\operatorname{ft} along the x x -axis?

24 ft ⁡ ⋅ lb ⁡ s 24\operatorname{ft}\cdot\operatorname{lb}s

120 ft ⁡ ⋅ lb ⁡ s 120\operatorname{ft}\cdot\operatorname{lb}s

72 ft ⁡ ⋅ lb ⁡ s 72\operatorname{ft}\cdot\operatorname{lb}s

48 ft ⁡ ⋅ lb ⁡ s 48\operatorname{ft}\cdot\operatorname{lb}s

10. Physics Applications of Integrals

Work

Calculus

10. Physics Applications of Integrals

Work

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Multiple Choice

How much work is required to push a chair across the floor with a force of $F equals 8 lb$ from $x equals 6 ft$ to $x equals 9 ft$ along the $x$ -axis?

$120 ft times lb of s$

$72 ft times lb of s$

$24 ft times lb of s$

$48 ft times lb of s$

Verified step by step guidance

Step 1: Recall the formula for work done when a constant force is applied over a distance. The work W is given by the formula: W = F * d, where F is the force and d is the distance over which the force is applied.

Step 2: Identify the given values in the problem. The force F is 8 lb, and the distance d is the difference between the final position (x = 9 ft) and the initial position (x = 6 ft).

Step 3: Calculate the distance d by subtracting the initial position from the final position: d = 9 ft - 6 ft.

Step 4: Substitute the values of F and d into the formula for work: W = F * d. This becomes W = 8 lb * (9 ft - 6 ft).

Step 5: Simplify the expression to find the work done. Ensure the units are consistent, and the result will be in ft⋅lb.

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