16. How much work is done on a bookshelf being pulled 4.00 m at an angle of 35.0„a from the horizontal? The magnitude of the component of the force that does the work is 87.0 N
Work =force*displacement*cos (angle between force and displacement)=87*4*cos35= 285 Joules.
I honestly don't know - help?
Well, it sounds like that bookshelf is getting quite the workout! Let's calculate the work done using a bit of humor!
To find the work done, we can use the formula:
Work = Force * Distance * cos(theta)
Now, let's substitute in the given values. We have a force of 87.0 N, a distance of 4.00 m, and an angle of 35.0°.
So, the work done is equal to 87.0 N times 4.00 m times the cosine of 35.0°.
But wait! Before we continue, have you ever tried to pull a bookshelf at an angle of 35.0°? It's quite a sight! You'll definitely get some interesting looks from bystanders.
Okay, back to the calculations. Let's find the cosine of 35.0°.
Cosine of 35.0° is approximately 0.8192.
Now, let's put it all together:
Work = 87.0 N * 4.00 m * 0.8192
And if we plug that into our trusty calculator, we get...
*drumroll please*
Work = 285.65 Joules!
So, the work done on the bookshelf is approximately 285.65 Joules. That's some serious effort!
But remember, it's always good to add a little bit of humor to your work. After all, who doesn't love a good bookshelf-pulling joke?
To find the work done on the bookshelf, we can use the formula:
Work = Force * Distance * cos(theta)
Where:
- Work is the amount of work done (in joules, J)
- Force is the magnitude of the component of the force that does the work (in newtons, N)
- Distance is the distance the bookshelf is pulled (in meters, m)
- Theta is the angle between the force and the direction of displacement (in degrees)
Given:
Force = 87.0 N
Distance = 4.00 m
Theta = 35.0°
Substituting the given values into the formula, we have:
Work = 87.0 N * 4.00 m * cos(35.0°)
To calculate this, we need to convert the angle into radians:
Radians = Degrees * (π / 180)
Radians = 35.0° * (π / 180) ≈ 0.6109 radians
Now we can calculate the work:
Work = 87.0 N * 4.00 m * cos(0.6109 radians)
Work = 87.0 N * 4.00 m * 0.8114
Work ≈ 281.3 J
Therefore, the work done on the bookshelf is approximately 281.3 joules (J).
To find the work done on a bookshelf, you can use the formula:
Work (W) = Force (F) * Distance (d) * Cosine (θ)
Where:
- Force (F) represents the component of the force that does the work.
- Distance (d) represents the distance the bookshelf is being pulled, which is 4.00 m in this case.
- Cosine (θ) represents the cosine of the angle between the force and the direction of the displacement, which is 35.0 degrees in this case.
Given that the force is 87.0 N, the distance is 4.00 m, and the angle is 35.0 degrees, we can now calculate the work done.
W = 87.0 N * 4.00 m * Cos(35.0°)
First, calculate the cosine of 35.0° using a calculator: Cos(35.0°) ≈ 0.819
W ≈ 87.0 N * 4.00 m * 0.819
W ≈ 284.856 J
Therefore, the work done on the bookshelf is approximately 284.856 Joules.