A 301-kg motorcycle is accelerating up along a ramp that is inclined 30.0º above the horizontal. The propulsion force pushing the motorcycle up the ramp is 3420 N, and air resistance produces a force of 230 N that opposes the motion. Find the magnitude of the motorcycle's acceleration.
x-axis is directed along F = 3420 N
x: ma=F –F(res) - mg•sinα,
a= (F-F(res)}/m - g•sin α =
=(3420-230)/301 – 9.8•sin30 =
= 5.7 m/s²
To find the magnitude of the motorcycle's acceleration, we can use Newton's second law of motion:
F_net = m * a
Where:
- F_net is the net force acting on the motorcycle
- m is the mass of the motorcycle
- a is the acceleration of the motorcycle
In this problem, the net force is the difference between the propulsion force and the force of air resistance:
F_net = F_propulsion - F_air_resistance
Substituting in the given values:
F_net = 3420 N - 230 N
= 3190 N
Now, we can solve for acceleration:
3190 N = 301 kg * a
Dividing both sides of the equation by 301 kg:
10.633 N/kg = a
Therefore, the magnitude of the motorcycle's acceleration is 10.633 m/s^2.