a 55kg skateboarder on a 3kg board starts coasting on level ground at 8 m/sec. Let k=3.2 kg/sec. About how far will the skater coast before reaching a complete stop?
To find out how far the skateboarder will coast before reaching a complete stop, we need to calculate the deceleration (negative acceleration) of the skateboarder. We can then use this deceleration to determine the distance traveled using the equation of motion.
The deceleration of the skateboarder can be found using Newton's second law of motion, which states that the force exerted on an object is equal to its mass multiplied by its acceleration. Since the only force acting on the skateboarder is friction, we can use the formula:
Force = mass * acceleration
The force of friction can be calculated using the equation:
Force = k * mass
where k is the coefficient of kinetic friction and is provided as 3.2 kg/sec.
Using the equations above, we can solve for the acceleration:
acceleration = (k * mass) / mass
Now we substitute the values into the equation:
acceleration = (3.2 kg/sec * 55 kg) / 55 kg
Simplifying:
acceleration = 3.2 kg/sec
The negative sign indicates deceleration (opposite direction of motion).
Next, we can use the equation of motion to find the distance traveled.
The equation of motion is given by:
Final velocity^2 = Initial velocity^2 + 2 * acceleration * distance
In this case, the initial velocity is 8 m/sec, the final velocity is 0 m/sec (since the skater stops), and the acceleration is -3.2 kg/sec.
0^2 = 8^2 + 2 * (-3.2 kg/sec) * distance
0 = 64 - 6.4 * distance
6.4 * distance = 64
distance = 64 / 6.4
distance = 10 meters
Therefore, the skateboarder will coast approximately 10 meters before coming to a complete stop.