I have a cart weighing 550g on a horizontal track with values for \\muK at .09 a

Question

I have a cart weighing 550g on a horizontal track with values for muK at .09 and muS at .15.No string or hnagar is attached this time. The cart is moved to the right end of the track at an angle of 5 degrees. Releasing the brakes shows the cart moves with a slight push/bump. The accelration recorded was .02452 m/s^2. After it is then placed at 7 degrees and pused with a slight bump and recorded to have acceleration of -.3166 m/s^2.

Whats the coefficient of kinetic friction of the trial at 5 degrees and at 7 degrees? Please show equations and answer in detail.

Explanation / Answer

at 5 degrees

ma = m*g*sin(5) - mu_k*m*g*cos(5)

a = g*(sin(5)-mu_k*cos(5))

0.2452 = 9.81*(0.0871-mu_k*0.996)

0.0249 = 0.0871-mu_k*0.996

mu_k = 0.0624
--------------------------------------

at 7 degrees angle

a =g*( mu_k*cos(7)-sin(7))

-0.3166 = 9.81*(mu_k*0.992 - 0.121)

mu_k = 0.089

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