Answer: 0.879
Step-by-step explanation:
To find the coefficient of kinetic friction between the block and the floor, we need to analyze the relationship between the applied force, the block's speed, and the frictional force.
First, let's determine the acceleration of the block. We can use the formula:
Force = mass * acceleration
Rearranging the formula, we have:
Acceleration = Force / mass
Plugging in the values, we get:
Acceleration = 37.0 N / 4.30 kg = 8.60 m/s^2
Next, let's examine the graph of the block's speed versus time. The slope of this graph represents the acceleration of the block. Since the graph is a straight line, we can find the slope by selecting two points on the line and calculating the change in speed divided by the change in time.
By looking at the graph, we can see that the speed changes from 0 m/s at t = 0 s to 3.50 m/s at t = 4.00 s.
The change in speed is 3.50 m/s - 0 m/s = 3.50 m/s
The change in time is 4.00 s - 0 s = 4.00 s
Now we can find the acceleration using these values:
Acceleration = Change in speed / Change in time
Acceleration = 3.50 m/s / 4.00 s = 0.875 m/s^2
Since the acceleration calculated from the applied force and the acceleration calculated from the graph are the same, we can conclude that the net force acting on the block is zero. This means that the frictional force must be equal in magnitude and opposite in direction to the applied force.
The frictional force can be calculated using the formula:
Force of friction = coefficient of friction * normal force
Since the block is on a horizontal floor, the normal force is equal to the weight of the block, which is given by:
Weight = mass * gravity
Plugging in the values, we have:
Weight = 4.30 kg * 9.8 m/s^2 = 42.14 N
Now we can find the coefficient of kinetic friction:
Coefficient of friction = Force of friction / normal force
Coefficient of friction = 37.0 N / 42.14 N = 0.879