Final answer:
To calculate the magnitude of the acceleration of the box moving down the ramp, we need to consider the forces acting on it. The force pushing the box down the ramp is equal to the force of gravity acting on the box (mg) multiplied by the sine of the angle of the ramp (sin(55°)). We can find the force of friction using the coefficient of kinetic friction (μk) and the normal force (mg) multiplied by the cosine of the angle of the ramp (cos(55°)). The net force on the box is equal to the force pushing it down the ramp minus the force of friction. Finally, we can use Newton's second law (F = ma) to calculate the acceleration.
Step-by-step explanation:
To calculate the magnitude of the acceleration of the box, we need to consider the forces acting on it. The force pushing the box down the ramp is equal to the force of gravity acting on the box (mg) multiplied by the sine of the angle of the ramp (sin(55°)). We can find the force of friction using the coefficient of kinetic friction (μk) and the normal force (mg) multiplied by the cosine of the angle of the ramp (cos(55°)). The net force on the box is equal to the force pushing it down the ramp minus the force of friction. Finally, we can use Newton's second law (F = ma) to calculate the acceleration. Plugging in the given values, we have:
Force pushing box down ramp = (15.0 kg)(9.8 m/s²)sin(55°) = 133.96 N
Force of friction = μk(mg)cos(55°) = (0.3)(15.0 kg)(9.8 m/s²)cos(55°) = 52.38 N
Net force = Force pushing box down ramp - Force of friction = 133.96 N - 52.38 N = 81.58 N
Acceleration = Net force / mass = 81.58 N / 15.0 kg = 5.44 m/s²