A gardener mows a lawn with an old-fashioned push mower. The handle of the mower makes an angle of 30 ∘ with the surface of the lawn. If a 50.0-N force is applied along the handle of the 15-kg mower, what is the normal force exerted by the lawn on the mower?
78.9 N
To find the normal force exerted by the lawn on the mower, we need to consider the forces acting on the mower.
1. The force applied along the handle of the mower is 50.0 N.
2. The weight of the mower acts downward, perpendicular to the surface of the lawn. The weight can be calculated as the mass of the mower multiplied by the acceleration due to gravity (9.8 m/s^2).
Weight = mass x acceleration due to gravity
Weight = 15 kg x 9.8 m/s^2
Now, let's resolve the force applied along the handle into its components.
The component of the applied force perpendicular to the surface of the lawn will be responsible for the normal force exerted by the lawn on the mower.
3. The angle between the applied force and the surface of the lawn is 30°. Therefore, the component of the applied force acting perpendicular to the surface can be calculated using the formula:
Perpendicular force = Applied force x sin(angle)
Now, let's calculate the perpendicular force:
Perpendicular force = 50.0 N x sin(30°)
Next, the normal force exerted by the lawn on the mower is equal and opposite to the perpendicular force.
Therefore, the normal force exerted by the lawn on the mower is equal to:
Normal force = Perpendicular force
Calculate the value of the perpendicular force and you will have the normal force exerted by the lawn on the mower.
To find the normal force exerted by the lawn on the mower, we need to consider the forces acting on the mower.
The force applied along the handle can be resolved into two components: the horizontal component and the vertical component. The horizontal component does not affect the normal force since it acts parallel to the surface of the lawn.
Now, let's calculate the vertical component of the force applied along the handle:
Vertical component = Force applied * sin(angle)
Here, the angle is given as 30 degrees and the force applied is 50.0 N. Plugging in the values, we get:
Vertical component = 50.0 N * sin(30∘)
Calculating this expression:
Vertical component = 50.0 N * 0.5
Vertical component = 25.0 N
Since the mower is on a flat surface, the normal force exerted by the lawn on the mower is equal to the weight of the mower. The weight is given by the equation:
Weight = Mass * Acceleration due to gravity
Here, the mass of the mower is given as 15 kg and the acceleration due to gravity is approximately 9.8 m/s². Plugging in the values, we get:
Weight = 15 kg * 9.8 m/s²
Weight = 147 N
Therefore, the normal force exerted by the lawn on the mower is 147 N.