Answer:
[tex]W = 724.89\ J[/tex]
Explanation:
given,
mass of the car = 200 Kg
speed = 3 m/s
radius of the circular path = 8 m
time t = 0
speed as O
Speed = 0.5 m/s
time = 4 s
work done = ?
initial angular velocity
[tex]P_1 = m v r_1[/tex]
[tex]P_1 = 200 \times 3 \times 8[/tex]
[tex]P_1 = 4800\ Kg m/s^2[/tex]
radius at 4 second
[tex]r_2 = r_1 - v_0\ t[/tex]
[tex]r_2 = 8 -4\times 0.5[/tex]
[tex]r_2 = 6\ m[/tex]
[tex]P_2 = m v_2 r_2[/tex]
[tex]P_2 = 200 \times v_2 \times6[/tex]
[tex]P_2= 1200v_2\ Kg m/s^2[/tex]
now,
[tex]1200v_2= 4800\ Kg m/s^2[/tex]
v₂ = 4 m/s
[tex]v' = \sqrt{4^2 + 0.5^2}[/tex]
v' = 4.031 m/s
work done
[tex]W = \dfrac{1}{2}m(v_f^2 - v^2)[/tex]
[tex]W = \dfrac{1}{2}\times 200 \times (4.031^2 - 3^2)[/tex]
[tex]W = 724.89\ J[/tex]
