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A woman pushes a 27 kg lawnmower at a steady speed. She exerts a 120 N force in a direction 35◦ below the horizontal. The acceleration of gravity is 9.8 m/ 2 . 27 kg 120 N 35◦ Find the magnitude of the vertical force this lawnmower exerts on the lawn. Answer in units of N.

Respuesta :

skyluke89

The vertical force exerted on the lawn is 68.8 N downward

Explanation:

The vertical force exerted by the lawnmower on the lawn is equal to the vertical component of the force applied, therefore:

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

where

F is the magnitude of the force applied

[tex]\theta[/tex] is the angle between the direction of the force and the horizontal

In this problem:

F = 120 N

[tex]\theta=-35^{\circ}[/tex]

Substituting,

[tex]F_y = (120)(sin 30)=-68.8 N[/tex]

where the negative sign means the direction of the force is downward.

Learn more about vector components and forces here:

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