Question

A gardener mows a lawn with an old-fashioned push mower. The handle of the i mower makes a 32° angle with the surface of the lawn.

a)If a 68N force is applied along the handle of the 17kg mower, what is the force exerted by the lawn on the mower? b）If the angle between the surface of the lawn and the handle of the mower is increased, does this force increase, decrease, or stay the same? Explain.

Answer 1

The force exerted by the lawn on the mower is 57.64N. Increasing the angle between the surface of the lawn and the handle of the mower will decrease the force exerted by the lawn on the mower.

Step-by-step explanation:

To calculate the force exerted by the lawn on the mower, we need to find the component of the applied force along the surface of the lawn. The force exerted by the lawn on the mower is equal in magnitude but opposite in direction to this component. Using trigonometry, we can find that the component of the applied force along the surface of the lawn is 68N * cos(32°) = 57.64N. Therefore, the force exerted by the lawn on the mower is 57.64N.

If the angle between the surface of the lawn and the handle of the mower is increased, the force exerted by the lawn on the mower will decrease. This is because as the angle increases, the component of the applied force along the surface of the lawn decreases. Therefore, the force exerted by the lawn on the mower will also decrease.