A 302 kg motorcycle is accelerating up along a ramp that is inclined 24° above the
horizontal. The propulsion force pushing the motorcycle up the ramp is 2860 N, and the
air resistance produces a force of 235 N that opposes the motion. Find the magnitude
of the motorcycle’s acceleration.
m*g = 302kg * 9.8N/kg = 2960 N. = Wt. of
motorcycle.
Fp = 2960*sin24 = 1204 N. = Force parallel to the ramp.
Fa = 235 N. = Force of air resistance.
a = (Fap-Fp-Fa)/m = (2860-1204-235)/302=
4.71 m/s^2
To find the magnitude of the motorcycle's acceleration, we can use Newton's second law of motion, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration.
First, let's break down the forces acting on the motorcycle. There are two forces acting along the ramp: the propulsion force pushing the motorcycle up the ramp and the force of air resistance opposing the motion. The vertical component of the propulsion force is canceled out by the normal force of the ramp, so we only need to consider the horizontal component of the propulsion force and the force of air resistance.
We need to resolve the propulsion force and the force of air resistance into their components along the ramp. Since the ramp is inclined at an angle of 24° above the horizontal, we can use trigonometry to calculate the horizontal components of these forces.
The horizontal component of the propulsion force is calculated as follows:
Propulsion force (horizontal) = Propulsion force * cos(angle)
Propulsion force (horizontal) = 2860 N * cos(24°)
The force of air resistance acts in the opposite direction to the horizontal motion, so its horizontal component will be negative:
Force of air resistance (horizontal) = - Force of air resistance * cos(angle)
Force of air resistance (horizontal) = - 235 N * cos(24°)
Now that we have the horizontal components of the forces, we can calculate the net force along the ramp by adding them together:
Net force (horizontal) = Propulsion force (horizontal) + Force of air resistance (horizontal)
Next, we can use Newton's second law to calculate the acceleration:
Net force (horizontal) = mass * acceleration
Now we can rearrange the equation to solve for the acceleration:
acceleration = Net force (horizontal) / mass
Substituting the values we calculated earlier:
acceleration = (Propulsion force (horizontal) + Force of air resistance (horizontal)) / mass
Finally, plug in the values and calculate the acceleration:
acceleration = (2860 N * cos(24°) - 235 N * cos(24°)) / 302 kg
Solving this equation will give you the magnitude of the motorcycle's acceleration.