Two people start running from rest. The first person has a mass of 59 kg and is wearing
dress shoes with a coefficient of static friction of 0.52. The other person is wearing
running shoes with a coefficient of static friction of 0.66.
Explain why we do not really need the mass of either person when finding the initial maximum possible acceleration.
force=mass*acceleration
mu*mg=m*a
a=mu*g
oh...
thank you
We do not really need the mass of either person when finding the initial maximum possible acceleration because the mass cancels out in the equation for calculating the maximum static frictional force.
The maximum static frictional force can be calculated using the equation:
F_static_max = μ * N
where:
- F_static_max is the maximum static frictional force
- μ is the coefficient of static friction
- N is the normal force (equal to the weight of the person)
The weight of a person can be calculated using the equation:
N = m * g
where:
- m is the mass of the person
- g is the acceleration due to gravity (approximately 9.8 m/s^2)
If we substitute this equation for N in the first equation, we get:
F_static_max = μ * (m * g)
Since the mass (m) appears on both sides of the equation, it cancels out, leaving:
F_static_max = μ * g
Therefore, the maximum static frictional force (and consequently the maximum acceleration) does not depend on the mass of the person.
When finding the initial maximum possible acceleration, we do not really need the mass of either person. This is because the maximum possible acceleration is determined by the coefficient of static friction, which represents the maximum amount of friction that can be generated between two surfaces before they start sliding against each other.
In this scenario, the coefficient of static friction is given for both individuals. The coefficient of static friction depends on the nature of the surface and the shoes being used. It indicates how much friction can be generated between the shoes and the ground before slipping occurs.
The maximum possible acceleration is limited by the maximum static friction force acting on the shoes. As long as the applied force on the shoes is below or equal to the maximum static friction force, the shoes will not slip.
Since the mass of the individuals affects the maximum static friction force (F_max = μ_s * N, where μ_s is the coefficient of static friction and N is the normal force), it may seem like we would need the mass to calculate it. However, in this scenario, we only need to compare the coefficients of static friction between the different shoes.
By comparing the coefficients of static friction for dress shoes (0.52) and running shoes (0.66), we can determine that the person wearing the running shoes has a higher maximum static friction force. This means that the person wearing the running shoes can achieve a higher maximum possible acceleration before their shoes start slipping compared to the person wearing dress shoes, regardless of their masses.
Therefore, in this case, the mass of either person is not needed when finding the initial maximum possible acceleration.