PS.2.1 Worked Example: Sliding Block

A diagram of the mass impacting the spring and then rebounding.

A block of mass \(\displaystyle m\) is sliding down an inclined plane of angle \(\displaystyle \theta\) with respect to the horizontal (left figure). At the bottom of the incline there is a spring. After compressing the spring the block stops momentarily and then it starts to slide up the incline as shown in the right figure. There is kinetic friction between the block and the inclined surface. The coefficient of kinetic friction is \(\displaystyle \mu _ k\) . The graviational force on the block is directed in the downward vertical direction. Consider the x-axis parallel to the incline surface and positive pointing down. Express your answers in terms of \(\displaystyle g\) , theta for \(\displaystyle \theta\) , and mu_k for \(\displaystyle \mu _ k\) as needed.

(Part a) What is the x-component of the block's acceleration vector when it is sliding down?

(Part b) What is the x-component of the block's acceleration vector when it is sliding up?

 

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