How much work is done on a bookshelf being pulled 5.00m at an angle of 37.0 degrees from the horizontal? The magnitude of the component of the force that does the work is 43.0N
Hi Julie,
To make an object to move, an external force need to be applied. The force/energy what you put on the object is converted in to some other form of the energy. In this case, the force that you apply is transformed into 'motion'. (neglecting friction/loss).
Work done = Force x Distance moved
Work done = 43 Cos37 x 5
Work done = 171.7N-m = 171.7Joules
Note: Here, I have considered horizantal component of force, because work is done in the direction of motion.
Hope this makes sense.
Thanks,
Jnanesha
Jnanesha.ks
at
quest-global
com
Well, it sounds like that bookshelf could use a good workout! If we break it down, the work done on the bookshelf can be found by multiplying the magnitude of the force (43.0N) by the distance it's being pulled (5.00m) and the cosine of the angle (37.0 degrees). So, using this formula, we can calculate the work done. However, I'm sensing a bit of stiffness in our calculations. Maybe it's time for some bookshelf yoga? Namaste!
To calculate the work done on the bookshelf, we can use the formula:
Work = Force * Distance * cosθ
where:
- Work is the amount of work done on the bookshelf,
- Force is the magnitude of the component of the force that does the work,
- Distance is the distance the bookshelf is pulled, and
- θ is the angle between the direction of force and the direction of displacement.
Given:
Force = 43.0 N,
Distance = 5.00 m,
θ = 37.0 degrees.
Step 1: Convert θ from degrees to radians.
θ (in radians) = θ (in degrees) * π / 180
θ (in radians) = 37.0 * π / 180
θ (in radians) ≈ 0.6458 radians
Step 2: Calculate the work done.
Work = 43.0 N * 5.00 m * cos(0.6458)
Work ≈ 43.0 N * 5.00 m * 0.8000
Work ≈ 172.0 Joules
Therefore, the work done on the bookshelf is approximately 172.0 Joules.
To find the work done on a bookshelf, you need to know the force applied and the displacement of the bookshelf. In this case, the force applied has a magnitude of 43.0N and the displacement is 5.00m at an angle of 37.0 degrees from the horizontal.
The work done on an object can be calculated using the formula:
Work = Force * Displacement * cos(theta)
Where:
- Work is the amount of work done (in joules, J)
- Force is the magnitude of the force applied (in newtons, N)
- Displacement is the distance the object moves (in meters, m)
- theta is the angle between the force and the displacement (in degrees)
In this case, the force and displacement values are given, so we can substitute them into the formula:
Work = 43.0N * 5.00m * cos(37.0 degrees)
Now, let's calculate the value of cos(37.0 degrees):
cos(37.0 degrees) = 0.7986
Substituting this value back into the formula:
Work = 43.0N * 5.00m * 0.7986
Calculating the final result:
Work = 170.957 J
Therefore, the amount of work done on the bookshelf is approximately 170.957 joules.