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Question: A particle of mass m, initially at rest is acted upon by a variable force F for a brief interval of ...

A particle of mass m, initially at rest is acted upon by a variable force F for a brief interval of time T. It begins to move with a velocity u after the force stops acting. F is shown in the graph as a function of time. The curve is a semicircle –

A

u = πF022 m\frac { \pi \mathrm { F } _ { 0 } ^ { 2 } } { 2 \mathrm {~m} }

B

u = πT28 m\frac { \pi \mathrm { T } ^ { 2 } } { 8 \mathrm {~m} }

C

u = πF0 T4 m\frac { \pi \mathrm { F } _ { 0 } \mathrm {~T} } { 4 \mathrm {~m} }

D

u = F0 T2 m\frac { \mathrm { F } _ { 0 } \mathrm {~T} } { 2 \mathrm {~m} }

Answer

u = πF0 T4 m\frac { \pi \mathrm { F } _ { 0 } \mathrm {~T} } { 4 \mathrm {~m} }

Explanation

Solution

Area under the F⃗−t\vec { F } - t curve = Impulse

π(F0)(T/2)2\frac { \pi \left( \mathrm { F } _ { 0 } \right) ( \mathrm { T } / 2 ) } { 2 } = mu – 0 Ž u = πF0 T4 m\frac { \pi \mathrm { F } _ { 0 } \mathrm {~T} } { 4 \mathrm {~m} }