91Ó°ÊÓ

When a motorcycle is on an inclined plane, like a ramp, gravity isn't pulling it directly straight down. Instead, we must consider the component of gravitational force that acts parallel to the ramp surface.
This is because gravity acts in a straight line to the ground, and the ramp creates an angle.
This component can be determined using the formula:

• \( F_{g, \text{ramp}} = mg \sin(\theta) \)

Here, *m* is the mass of the motorcycle, *g* is the acceleration due to gravity, typically estimated as \( 9.81 \space \text{m/s}^2 \), and \( \theta \) is the angle of the incline.
For the given motorcycle situation, the gravitational force component acting down the ramp was calculated as 1429.74 N. This means the gravity effect that tries to pull the motorcycle back down the ramp.

Net force is the total force acting on an object after all opposing forces have been subtracted.
In this scenario, the motorcycle is experiencing multiple forces:

• The propulsion force, which is 3150 N, works to push the bike up the ramp.
• The force of air resistance, opposing that motion, which is 250 N.
• The gravitational force component, which tries to pull the motorcycle back down the ramp, calculated as 1429.74 N.

To find the net force, first, we account for propulsion and air resistance:

• \( F_{ ext{net}} = 3150 \, \text{N} - 250 \, \text{N} = 2900 \, \text{N} \)

Then, subtract the gravitational force component:

• \( F_{ ext{total net}} = 2900 \, \text{N} - 1429.74 \, \text{N} = 1470.26 \, \text{N} \)

This net force dictates the motorcycle's motion along the incline.

An inclined plane is essentially a sloped surface, like a ramp, that allows an object to elevate against gravity with extended space but less force.
The angle of the incline affects how much the gravitational force component takes part in pulling back the object down the slope.
Key points when dealing with inclined planes include:

• The angle \(\theta\) of the incline, which influences the gravitational force component.
• The surface of the plane can also add frictional force affecting motion, though in this problem it is not mentioned.

By analyzing forces on an inclined plane, we can determine how these forces affect an object's movement up or down the slope.

The process of calculating acceleration involves combining all contributing forces and applying Newton's Second Law of Motion.
This law is elegantly expressed as:

• \( F = ma \)

Where:

• *F* is the total force acting on the object
• *m* is the mass of the object, given as 292 kg for the motorcycle
• *a* is the acceleration, which we wish to determine.

Rearranging for acceleration gives:

• \( a = \frac{F_{\text{total net}}}{m} \)

Plugging in our values, from the net force calculation we have:

• \( a = \frac{1470.26 \, \text{N}}{292 \, \text{kg}} \approx 5.034 \, \text{m/s}^2 \)

Thus, the motorcycle accelerates up the ramp at approximately 5.034 m/s².