3.3) I'm not sure whether it is correct or not. I'm am confused because of the Applied Force being at an angle. Am I only working out Fx and would I need to make use of trigonometry to determine F?   Fnet = ma F - Ff = 50(0) F - (uk * Fn) = 0 F- (uk * m * g) = 0 F - (0,4 * 50 * 9,8) = 0 F = 16N right    

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There are some mistakes in your solution. First, the transition from `F_f` to `mu*mg` is incorrect. We know that `F_f=mu*N,` where `N` is the reaction force. But in this case `N!=mg` because `F` acts partly upwards. We have to consider the both projections, vertical and horizontal.

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Hello!

There are some mistakes in your solution. First, the transition from `F_f` to `mu*mg` is incorrect. We know that `F_f=mu*N,` where `N` is the reaction force. But in this case `N!=mg` because `F` acts partly upwards. We have to consider the both projections, vertical and horizontal.

 

For the vertical axis we obtain  `N-mg+F*sin(alpha)=0`

and from the horizontal  `F*cos(alpha)-F_(f) =F*cos(alpha)-mu*N=0.`

 

Express `N` from the first equation and substitute it into the second:

`N=mg-Fsin(alpha),`

`Fcos(alpha)=mu(mg-Fsin(alpha))=mu mg-F mu sin(alpha).`

So  `F(cos(alpha)+mu sin(alpha))=mu mg`  and the final formula is

`F=(mu mg)/(cos(alpha)+mu sin(alpha)).`

 

 

Now recall that `alpha`=20°, `mu=0.4,` `m`=50 kg and `g`=9.8 `m/s^2,` and compute:

`F approx (0.4*50*9.8)/(0.94+0.4*0.34) approx 196/1.08 approx` 181 (N). This is the answer for 3.3. Now you can easily solve 3.4 and 3.5.

 

Note also that 0.4*50*9.8 = 196 and not 16 as you wrote (maybe you simply omitted 9).

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