A 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 (a) the net force on the rider and (b) the force on the rider from the motorcycle?
66*(2*cos5) for a.
not sure for b.
To find the magnitude of the net force on the rider and the force on the rider from the motorcycle, we can break down the forces acting on the rider.
Let's start with the gravitational force acting on the rider. The weight of the rider can be calculated using the formula W = m * g, where m is the mass of the rider and g is the acceleration due to gravity (approximately 9.8 m/s^2).
Given that the mass of the rider is 66.0 kg, we can calculate the weight of the rider:
W_rider = m * g = 66.0 kg * 9.8 m/s^2 = 646.8 N
Next, let's calculate the component of the weight force acting parallel to the ramp. This force is responsible for the acceleration of the rider up the ramp. We can find it using the formula F_parallel = W * sin(θ), where θ is the angle of the ramp (5.0° in this case).
F_parallel = 646.8 N * sin(5.0°) = 56.43 N
Since the rider is accelerating up the ramp at 2.0 m/s^2, there must be an additional force acting on the rider in the same direction as the acceleration. This force is provided by the net force.
To find the magnitude of the net force on the rider, we can use Newton's second law: F_net = m * a, where a is the acceleration.
F_net = 66.0 kg * 2.0 m/s^2 = 132.0 N
Now, to find the force on the rider from the motorcycle, we can subtract the weight component parallel to the ramp from the net force.
F_motorcycle = F_net - F_parallel = 132.0 N - 56.43 N = 75.57 N
Therefore, the magnitude of the net force on the rider is 132.0 N, and the magnitude of the force on the rider from the motorcycle is 75.57 N.