motorcycle and 66.0 kg rider accelerate at 2.0 m/s2 up a ramp inclined 5.0° above the horizontal. What are the magnitude of the force on the rider from the motorcycle?

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To find the magnitude of the force on the rider from the motorcycle, we need to consider the forces acting on the rider.

First, let's break down the forces acting on the rider along the incline of the ramp:

- The component of the rider's weight acting down the incline (Wx): This force can be calculated using the formula Wx = mg sin(θ), where m is the mass of the rider (66.0 kg), g is the acceleration due to gravity (9.8 m/s^2), and θ is the angle of the incline (5.0°). Substituting the given values, we have Wx = (66.0 kg)(9.8 m/s^2) sin(5.0°).

Now, let's consider the net force acting on the rider along the incline, which is responsible for accelerating the rider:

- The net force (Fnet): This force can be calculated using Newton's second law, Fnet = m * a, where m is the mass of the rider (66.0 kg) and a is the acceleration (2.0 m/s^2).

The net force can be further broken down into two components:

- The parallel component of the net force along the incline (Fpar): This is the component of the net force that acts parallel to the incline. Fpar = Fnet x cos(θ), where θ is the angle of the incline (5.0°).

- The perpendicular component of the net force along the incline (Fperp): This is the component of the net force that acts perpendicular to the incline. Fperp = Fnet x sin(θ), where θ is the angle of the incline (5.0°).

Since we want to find the magnitude of the force on the rider from the motorcycle, we are interested in the perpendicular component of the net force. Therefore, the force magnitude on the rider from the motorcycle can be calculated using the formula:

Force magnitude = |Fperp - Wx|

Substituting the given values into the equations, we can calculate the magnitude of the force on the rider from the motorcycle.