A box slides down a 26° ramp with an acceleration of 1.19 m/s2. Determine the coefficient of kinetic friction between the box and the ramp.
μk =
To determine the coefficient of kinetic friction (μk) between the box and the ramp, we can use the following equation:
μk = tan(θ) - (a/g)
where:
- θ is the angle of the ramp (26° in this case)
- a is the acceleration of the box (1.19 m/s^2 in this case)
- g is the acceleration due to gravity (approximately 9.8 m/s^2)
Now let's plug in the values into the equation to calculate μk:
μk = tan(26°) - (1.19 m/s^2 / 9.8 m/s^2)
Using a scientific calculator, we can find the tangent of 26°, which is approximately 0.4877. Now let's substitute this value:
μk = 0.4877 - (1.19 m/s^2 / 9.8 m/s^2)
Evaluating the division:
μk = 0.4877 - 0.1214
Finally, subtracting the values:
μk = 0.3663
Therefore, the coefficient of kinetic friction between the box and the ramp is approximately 0.3663.