Final answer:
To find the mass of the bag of coal, we use Newton's second law, factoring in the applied force, the force of kinetic friction, and the acceleration due to gravity. By solving the resulting equation, we determine the mass of the bag.
Step-by-step explanation:
The question asks to find the mass of a bag of coal that St. Nicholas is dragging when a horizontal force of 130 N is applied, causing a net acceleration of 1.8 m/s2, and the coefficient of kinetic friction between the bag and the pavement is 0.158. We start by identifying the forces acting on the bag. There's the applied horizontal force (Fa) of 130 N and the force of kinetic friction (Ff) opposing the movement.
The force of kinetic friction can be calculated using the equation Ff = μk × N, where μk is the coefficient of kinetic friction and N is the normal force. The normal force (N) in this case is equal to the weight of the bag since it's on a horizontal plane, so N = m × g, where m is the mass of the bag and g is the acceleration due to gravity, which is approximately 9.8 m/s2.
To find the mass, we can set up the equation for Newton's second law, where the net force is the applied force minus the frictional force (Fa - Ff = m × a). We have Fa = 130 N, μk = 0.158, a = 1.8 m/s2, and g = 9.8 m/s2. Solving for m gives us m = (Fa - (μk × m × g)) / a. After rearranging, we find m = Fa / (a + μk × g), which yields the mass of the bag of coal.