m g sin T = u m g cos T
sin T = u cos g
tan T = u
if u = 1.5
tan T = 1.5
T = tan^-1 1.5 = 56.3 degrees
I am trying to help my son with his math, but I am stuck!
The advertisement for a new shoe promises runners less slip. The coefficient of friction (μ) between concrete and a new material used in the sole of this shoe is 1.5. The force of friction that causes slip is equal to mg sinθ, where m is a runner’s mass and g is the acceleration due to gravity. The force that prevents slip is μmg cosθ.
At the instant of slip, the force that causes slip is equal to the force that prevents it. Write an equation to show this relationship.
Rewrite the equation with trigonometric expressions on one side of the equation, and substitute the coefficient of friction for the new material.
Use a trigonometric identity to rewrite the equation using only the tangent function.
Solve for θ, the angle at which the new shoe will start to slip.
46.3 deg
53.5
56.3 deg
59.2
1 answer
2 answers