Question

13 A lawn-mower is pushed with a force of 50 N.

If the angle between the handle of the mower
and the ground is 30°,
(i) Calculate the magnitude of the force that
is pressing the lawn-mower directly into
the ground.
(ii) Calculate the magnitude of the effective
force that moves the mower forward.
(iii) Why does the lawn-mower move forward
and not downward into the ground?​

Answer 1

13. (i) The magnitude of the force that is pressing the lawn-mower directly into the ground is 25 N

(ii) The magnitude of the effective force that moves the mower forward is approximately 43.3 N

(iii) Because there are no net downward force acting on the lawn-mower

Step-by-step explanation:

13. The given force pushing the lawn-mower = 50 N

The angle at which the force acts = 30° to the ground

The component of the pushing force are;

(i) The magnitude of the force that is pressing the lawn-mower directly into the ground = The vertical component of the pushing force

The vertical component of the pushing force,
`F_y` = 50 N × sin(30°) = 25 N

∴ The magnitude of the force that is pressing the lawn-mower directly into the ground =
`F_y` = 25 N

(ii) The magnitude of the effective force that moves the mower forward = The horizontal component of the pushing force

The horizontal component of the pushing force, Fₓ = 50 N × cos(30°) = 25·√3 N ≈ 43.3 N

∴ The magnitude of the effective force that moves the mower forward = 25·√3 N ≈ 43.3 N

(iii) The lawn mower moves forward and not downwards because according to Newton's first Law of motion, the lawn-mower moves forward because it is being acted on by a net forward directed horizontal force

However, according to Newton's third law, the reaction of the ground is equal to the weight of the lawn mower, therefore, there are no net vertical force acting on the lawn-mower, such that the lawn-mower remains in the initial horizontal level and does not move downward into the ground.