29.
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Answer: Total work done on the block is 3670.5 Joules.
Step by step:
Work done:
With F the force, d the displacement, and theta the angle of action (which is 0 since the block is pushed along the direction of displacement, and cos 0 = 1)
Given:
F = 75 N
m = 31.8 kg
Final velocity
In order to calculate the Work we need to determine the displacement, or distance the block travels. We can use the information about F and m to first figure out the acceleration:
Now we can determine the displacement from the following formula:
Here, the initial displacement is 0 and initial velocity is also 0 (at rest):
Now we still have "t" as unknown. But we are given one more bit of information from which this can be determined:
(using vf as final velocity, and tf as final time)
So it takes about 6.44 seconds for the block to move. This allows us to finally calculate the displacement:
and the corresponding work: