a coin rests on a book. the book tilts until the coin just begins to move. the angle is 17 degrees. what is the coefficient of static friction?
To determine the coefficient of static friction, we can use the equation:
μs = tan(θ)
where:
μs is the coefficient of static friction,
θ is the angle of inclination.
In this case, the angle of inclination is given as 17 degrees, so we can substitute it into the equation:
μs = tan(17°)
Calculating the value using a calculator:
μs ≈ tan(17°) ≈ 0.307
Therefore, the coefficient of static friction is approximately 0.307.
To determine the coefficient of static friction, we need to use the relationship between the coefficient of static friction and the angle at which an object starts to move. Here's how you can find the coefficient of static friction step by step:
1. Draw a free-body diagram: On the diagram, identify all the forces acting on the coin. In this case, there are two forces: the force due to gravity (mg), acting vertically downward, and the normal force (N) perpendicular to the surface of the book.
2. Resolve the forces into components: Since the coin is on an inclined surface, separate the force due to gravity into two components: one parallel to the surface (mg sinθ, where θ is the angle of inclination) and one perpendicular to the surface (mg cosθ).
3. Determine the force required to overcome static friction: The coin just begins to move when the component of the force due to gravity parallel to the surface (mg sinθ) overcomes the force of static friction (fs) acting in the opposite direction. Therefore, fs = mg sinθ.
4. Calculate the normal force: The normal force (N) is equal to the component of the force due to gravity perpendicular to the surface (mg cosθ). So, N = mg cosθ.
5. Apply the equation for static friction: The force of static friction (fs) is given by the equation fs = μsN, where μs is the coefficient of static friction.
6. Substitute the known values: Substitute fs = mg sinθ and N = mg cosθ into the equation fs = μsN to obtain μs.
In this case, the angle of inclination is given as 17 degrees. So, the coefficient of static friction can be calculated as follows:
μs = (mg sinθ) / (mg cosθ)
μs = tanθ
Substitute θ = 17 degrees:
μs = tan(17°)
Now you can use a calculator to find the value of tan(17°). After calculating, the value of the coefficient of static friction will be obtained.
When the coin starts to slip, the friction force mu*cos17*M*g
is equal to the component of the weight down the incline, M*g sin 17.
Solve for mu, the coefficient of statice friction. The M (mass)and g (acceleration of gravity) terms will cancel out.