To determine the mass in this scenario, we can rearrange the equation you mentioned:
μ * m * g = m * v^2 / (2 * d)
Where:
μ is the coefficient of static friction (given as 0.27)
m is the mass of the crates
g is the acceleration due to gravity (approximated as 9.8 m/s^2)
v is the velocity of the train (converted to m/s, which is 59.7 km/hr * 1000 m/km / 3600 s/hr)
By simplifying the equation, we can isolate the mass:
μ * g = v^2 / (2 * d)
μ * g = v^2 / (2 * m * a)
μ * g = v^2 / (2 * m * (v^2 / (2 * d)))
Simplifying further, we get:
μ * g * m * (v^2 / (2 * d)) = v^2
μ * g * m * v^2 / (2 * d) = v^2
μ * g * m = 2 * d
Now, we can solve for m:
m = (2 * d) / (μ * g)
Plug in the known values for μ (0.27) and g (9.8 m/s^2), and you'll be able to calculate the mass of the crates.