Question

A gardener pushes a lawn mower by applying a force of 150 newtons (N) to the handle. If the lawn mower handle makes a 38° angle with the ground, what is the force:

a. parallel to the ground?
b. perpendicular to the ground?

Answer 1

The force parallel to the ground is approximately 118.2 N, and the force perpendicular to the ground is approximately 92.355 N, calculated using trigonometric functions of the given angle.

Step-by-step explanation:

The force exerted by the gardener on the lawn mower can be resolved into two components: force parallel to the ground (horizontal) and force perpendicular to the ground (vertical). To find these components, we use trigonometry, specifically the sine and cosine functions. The horizontal component (parallel to the ground) is calculated using the cosine of the angle, while the vertical component (perpendicular to the ground) is calculated using the sine of the angle.

To calculate the force parallel to the ground:

• Fhorizontal = F × cos(θ)
• Fhorizontal = 150 N × cos(38°)
• Fhorizontal = 150 N × 0.7880 (approx.)
• Fhorizontal = 118.2 N (approx.)

To calculate the force perpendicular to the ground:

• Fvertical = F × sin(θ)
• Fvertical = 150 N × sin(38°)
• Fvertical = 150 N × 0.6157 (approx.)
• Fvertical = 92.355 N (approx.)

Therefore, the force parallel to the ground is approximately 118.2 N and the force perpendicular to the ground is approximately 92.355 N.