a truck of mass 8500Kg is pulling a trailer of mass 27 000Kg on a level road.The coefficient of kinetic friction is 0,20.A horizontal force of 75 000N moves the truck forward.question:calculate the magnitude of the acceleration of the system
To calculate the magnitude of the acceleration of the system, we need to consider the forces acting on the system.
1. The force applied by the truck: The horizontal force of 75,000N moves the truck forward. This force will accelerate the entire system.
2. The force of friction: The coefficient of kinetic friction is given as 0.20. To calculate the force of friction, we need to multiply the coefficient of friction by the weight of the trailer. The weight of the trailer can be calculated by multiplying its mass (27,000 kg) by the acceleration due to gravity (9.8 m/s^2).
Now, let's calculate the forces:
Force applied by the truck = 75,000N
Force of friction = (coefficient of kinetic friction) * (weight of the trailer) = 0.20 * (27,000 kg * 9.8 m/s^2)
Next, let's calculate the net force acting on the system:
Net force = Force applied by the truck - Force of friction
Now, we can use Newton's second law of motion, which states that the net force acting on an object is equal to its mass multiplied by its acceleration:
Net force = (total mass of the system) * (acceleration)
Rearranging the equation, we can solve for the acceleration:
Acceleration = Net force / (total mass of the system)
Substituting the values we calculated:
Acceleration = (75,000N - 0.20 * 27,000 kg * 9.8 m/s^2) / (8,500 kg + 27,000 kg)
Simplifying the equation will give you the magnitude of the acceleration of the system.