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Consider a lawnmower of mass m which can slide across a horizontal surface with a coefficient of friction μ. in this problem the lawnmower is pushed using a massless handle, which makes an angle θ with the horizontal. assume that fh, the force exerted by the handle, is parallel to the handle. take the positive x direction to be to the right and the positive y direction to be upward. use g for the magnitude of the acceleration due to gravity.

Respuesta :

Applied force is Fh at an angle theta with the horizontal

now we will have its components

[tex]F_x = F_h cos\theta[/tex]

[tex]F_y = F_h sin\theta[/tex]

now in order to find the normal force

we will have

[tex]N = mg + F_h sin\theta[/tex]

now we can find friction force

[tex]F_f = \mu N[/tex]

[tex]F_f = \mu * (mg + F_h sin\theta)[/tex]

now in order to move the lawn mover

[tex]F_hcos\theta = F_f[/tex]

[tex]F_h cos\theta = \mu *(mg + F_h sin\theta)[/tex]

now we will have

[tex]F_h(cos\theta - \mu sin\theta) = \mu mg[/tex]

[tex]F_h = \frac{\mu mg}{cos\theta - \mu sin\theta}[/tex]

so above is the force on it

ajeigbeibraheem

The magnitude [tex]\mathbf{f_h }[/tex] of the force required to slide the lawnmower over the ground is [tex]\mathbf{F_h = \dfrac{\mu mg}{(cos \theta - \mu sin \theta)}}[/tex]

Consider the movement of the lawnmower of mass (m) which slides across a horizontal surface in the horizontal direction;

In the horizontal direction, the net force is:

[tex]\mathbf{- F_h cos \theta + \mu N = 0}[/tex]

where;

  • [tex]f_h =[/tex] the force exerted by the handle

In the vertical direction, the net force is:

[tex]\mathbf{mg +F_h sin \theta = N}[/tex]

replacing the value of N in the second expression into the first part, then we have:

[tex]\mathbf{- F_h cos \theta + \mu N = 0}[/tex]

[tex]\mathbf{F_h cos \theta = \mu N}[/tex]

[tex]\mathbf{F_h cos \theta = \mu (mg +F_h sin \theta)}[/tex]

[tex]\mathbf{F_h (cos \theta- \mu sin \theta ) = \mu mg }[/tex]

[tex]\mathbf{F_h = \dfrac{ \mu mg }{(cos \theta- \mu sin \theta )}}[/tex]

Therefore, we can conclude that the magnitude [tex]\mathbf{f_h }[/tex] of the force required to slide the lawnmower over the ground is [tex]\mathbf{F_h = \dfrac{\mu mg}{(cos \theta - \mu sin \theta)}}[/tex]

Learn more about the magnitude of the force here:

https://brainly.com/question/9774180?referrer=searchResults

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