Determine the time time tB, tC, and tD needed for a block of mass m to slide from rest at A to points B, C, and D, respectively. Neglect effects of friction.
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The force that makes the box slide downwards is the component of the gravitational force that is parallel to the incline.
The acceleration of the box can be obtained using Newton's second law:
An accelerating object's position (x) as a function of time (t) is:
Where x0 and v0 are the initial position and velocity respectively. Setting the initial point (A) as x0=0, and since the block starts from rest (v0=0) the equation becomes:
Solving for t:
Thus the time the box needs to get from point A to B (distance b) is:
The time the box needs to get from point A to C (distance c) is:
The time the box needs to get from point A to D (distance d) is:
We get:© BrainMass Inc. brainmass.com December 24, 2021, 5:06 pm ad1c9bdddf>