Question

a 10 kg mass moves along x-axis its acceleration as a function of its position is shown in the figure what is the total work done on the mass by the force as mass moves from x =0 to x=8 cm

Answer 1

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Answer 2

Therefore workdone on the mass by the force is 8 × 10¯² J .

Given : a 10 kg mass moves along x-axis its acceleration as a function of its position is shown in the figure.

To find : Total work done on the mass by the force as mass moves from X = 0 to X = 8cm.

solution : from graph, it is clear that acceleration is directly proportional to displacement.

i.e., a ∝ x

⇒a = kx

where k is slope of graph.

k = (20 - 0)/(8 - 0) = 2.5

so, a = 2.5x

now force = ma = 10 × 2.5x = 25x

work done on he mass , W = ∫F dx

= 25∫x dx

= 25 [x²/2]

= 25 [ (8 × 10¯²)²/2 - 0²/2]

= 25 × 32 × 10¯⁴

= 8 × 10¯² J

Therefore workdone on the mass by the force is 8 × 10¯² J .