a) The custodian needs to apply 200 N of force
b) The custodian needs to apply 115.4 N of force
Explanation:
a)
We can solve this problem by applying Newton's second law: in fact, the net force along the horizontal direction must be equal to the product between the mass of the desk and the horizontal acceleration. Mathematically,
![F_x = ma_x](https://tex.z-dn.net/?f=F_x%20%3D%20ma_x)
where
is the net force on the horizontal direction, with F being the magnitude of the force applied by the custodian, and
the angle at which the force is applied
m is the mass of the desk
is the horizontal acceleration
In this problem we have:
m = 100 kg
![a_x = 1.0 m/s^2](https://tex.z-dn.net/?f=a_x%20%3D%201.0%20m%2Fs%5E2)
Solving for F, we find the force that the custodian must apply:
![F=\frac{ma_x}{cos \theta}=\frac{(100)(1.0)}{cos 60^{\circ}}=200 N](https://tex.z-dn.net/?f=F%3D%5Cfrac%7Bma_x%7D%7Bcos%20%5Ctheta%7D%3D%5Cfrac%7B%28100%29%281.0%29%7D%7Bcos%2060%5E%7B%5Ccirc%7D%7D%3D200%20N)
b)
In this case, the rope has an angle of
with the horizontal: this means that the force is applied at an angle of
with the horizontal.
As before, we can apply Newton's second law:
![F_x = ma_x](https://tex.z-dn.net/?f=F_x%20%3D%20ma_x)
And we have again
m = 100 kg (mass of the desk)
(horizontal acceleration)
This can be rewritten as
![Fcos \theta = ma_x](https://tex.z-dn.net/?f=Fcos%20%5Ctheta%20%3D%20ma_x)
And solving for F, we find
![F=\frac{ma_x}{cos \theta}=\frac{(100)(1.0)}{cos 30^{\circ}}=115.4 N](https://tex.z-dn.net/?f=F%3D%5Cfrac%7Bma_x%7D%7Bcos%20%5Ctheta%7D%3D%5Cfrac%7B%28100%29%281.0%29%7D%7Bcos%2030%5E%7B%5Ccirc%7D%7D%3D115.4%20N)
Learn more about Newton's second law:
brainly.com/question/3820012
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