A box slides down a 37° ramp with an acceleration of 1.24 m/s2. Determine the coefficient of kinetic friction between the box and the ramp.
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To determine the coefficient of kinetic friction between the box and the ramp, we need to use the following formula:
μk = tan(θ) - a/g
Where:
μk is the coefficient of kinetic friction
θ is the angle of the ramp (37° in this case)
a is the acceleration of the box (1.24 m/s^2)
g is the acceleration due to gravity (approximately 9.8 m/s^2)
Now, we can plug in the values into the formula:
μk = tan(37°) - 1.24/9.8
To find the value of tan(37°), we can use a scientific calculator or look it up in a trigonometric table. Plugging in the value, we have:
μk = 0.753 - 0.1265
Simplifying further, we get:
μk = 0.6265
Therefore, the coefficient of kinetic friction between the box and the ramp is approximately 0.6265.