A cyclist is riding in the positive horizontal direction at 14.8 m/s on a horizontal level surface. He encounters an air resistance force of 50 N. The actions on the pedals by the cyclist cause a backward force of 73 N to be exerted by the rear wheel on the ground. The mass of the cyclist-bike system is 89 kg. calculate the horizontal acceleration of the center of mass of the system.
The net force on the bike and rider is
Fnet = 73 - 50 = 23 N.
The acceleration is a = Fnet/m = 23/89 = 0.258 m/s^2
The 73 N backward force of the bike on the road is another way of saying that the road pushes the bike tires forward with that force. That is because of Newton's third law.
To calculate the horizontal acceleration of the center of mass of the system, we need to first find the net force acting on the cyclist-bike system in the horizontal direction. The net force can be determined using Newton's second law of motion, which states that the net force equals the product of mass and acceleration:
Net force = mass × acceleration
In this case, the mass of the cyclist-bike system is given as 89 kg. To determine the net force, we need to consider the forces acting on the system. There are two forces in this scenario: the air resistance force and the backward force exerted by the rear wheel.
The air resistance force is given as 50 N, but since it acts in the opposite direction to the motion of the cyclist, we should consider it as negative:
Air resistance force = -50 N
The backward force exerted by the rear wheel is given as 73 N, but because it also acts in the opposite direction to the motion, we should consider it as negative as well:
Backward force = -73 N
Next, to find the net force, we need to sum up the forces acting on the system:
Net force = Air resistance force + Backward force
= -50 N + (-73 N)
= -123 N
Now, we can use the formula Net force = mass × acceleration to solve for the acceleration of the system:
-123 N = 89 kg × acceleration
To isolate the acceleration, we need to divide both sides of the equation by the mass:
acceleration = -123 N / 89 kg
≈ -1.38 m/s²
The negative sign indicates that the acceleration is in the opposite direction to the motion. Therefore, the horizontal acceleration of the center of mass of the system is approximately -1.38 m/s².