Allison is skateboarding across a level road. The coefficient of static friction is 0.680 between Allison's shoes and the skateboard. If there is a hole in the road 23.2 m up ahead and Allison is able to stop without sliding off of the skateboard, what is the maximum velocity she could have initially been travelling?
To determine the maximum velocity Allison could have initially been traveling, we need to consider the forces acting on her while she is skateboarding.
The maximum static friction force, F_max, that can be exerted between her shoes and the skateboard can be calculated using the formula:
F_max = μ * N
Where:
- μ is the coefficient of static friction (given as 0.680)
- N is the normal force acting on Allison
The normal force, N, can be calculated as the weight of Allison, given by:
N = m * g
Where:
- m is Allison's mass (which is not given in the question)
- g is the acceleration due to gravity (approximately 9.8 m/s^2)
Since we don't have the mass of Allison, we can express the maximum static friction force as a multiple of the weight, using the coefficient of friction:
F_max = μ * m * g
To find the maximum velocity, we can use the work-energy principle. The work done by friction is equal to the change in kinetic energy:
Friction force * distance = (1/2) * m * V^2
Where:
- V is the final velocity, which is 0 because Allison stops
- The distance is 23.2 m
So, we can rewrite the equation as:
μ * m * g * distance = (1/2) * m * 0^2
Simplifying the equation, we get:
μ * g * distance = 0
Since the right side of the equation is 0, we can remove it:
μ * g * distance = 0
Now we can solve for the maximum velocity by rearranging the equation:
V = √(2 * μ * g * distance)
Substituting the given values:
V = √(2 * 0.680 * 9.8 * 23.2)
Calculating the expression:
V ≈ 10.35 m/s
Therefore, the maximum velocity Allison could have initially been traveling is approximately 10.35 m/s.