if a toy car's motor propelled it 1.905m in 7.1 seconds and it kept rolling .38m for 8.6 seconds what is the coefficient of friction between the wheels and the floor assuming that is the only source of friction.
i know accel=.08m/s2 and -.12m/s2 but after that i got lost.
To find the coefficient of friction between the wheels and the floor, we can use the equation:
frictional force = mass x acceleration
First, let's find the mass of the toy car. We know that the toy car's motor propelled it for 1.905m in 7.1 seconds with an acceleration of 0.08m/s^2. We can use the equation:
distance = initial velocity * time + (1/2) * acceleration * time^2
1.905m = 0 * 7.1s + (1/2) * 0.08m/s^2 * (7.1s)^2
Simplifying the equation gives us:
1.905m = (0.08m/s^2) * (0.5) * (7.1s)^2
1.905m = 0.04m/s^2 * (7.1s)^2
Now we can solve for the mass:
mass = 1.905m / (0.04m/s^2 * (7.1s)^2)
Next, we need to find the force that kept the toy car rolling for an additional 0.38m in 8.6 seconds. Since the toy car was already in motion, the force needed to overcome friction must be equal to the frictional force acting on the car.
The frictional force can be calculated using:
frictional force = mass x acceleration
We have calculated the mass, and the acceleration can be determined by using the equation:
acceleration = (final velocity - initial velocity) / time
Since the toy car is slowing down, the final velocity is 0m/s. The initial velocity can be obtained using the distance equation:
distance = initial velocity * time + (1/2) * acceleration * time^2
0.38m = initial velocity * 8.6s + (1/2) * acceleration * (8.6s)^2
Simplifying the equation gives us:
0.38m = initial velocity * 8.6s + (0.5) * acceleration * (8.6s)^2
Now we can solve for the initial velocity:
initial velocity = (0.38m - (0.5) * acceleration * (8.6s)^2) / 8.6s
Finally, we can calculate the frictional force by multiplying the mass by the acceleration:
frictional force = mass * acceleration
Once we have the frictional force, we can use the equation:
frictional force = coefficient of friction * normal force
Since the normal force is the force pushing the toy car onto the floor, which is equal to the toy car's weight, we can rewrite the equation as:
frictional force = coefficient of friction * weight
From here, we can solve for the coefficient of friction:
coefficient of friction = frictional force / weight
By plugging in the values, we should be able to find the coefficient of friction between the wheels and the floor.