Calculating Centripetal Acceleration and Force on Child

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Centripetal acceleration for a child moving at 1.50 m/s and 7.8 m from the center of a merry-go-round is calculated using the formula a = v²/r, resulting in 0.29 m/s². The net horizontal force exerted on the child is found using Fc = mv²/r, yielding a force of approximately 7.21 x 10^4 N. The calculations confirm the correct application of the formulas for centripetal motion. The discussion emphasizes the importance of using proper units and ensuring calculations are accurate. Overall, the problem illustrates the principles of centripetal acceleration and force in a practical scenario.
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Homework Statement


A child (mass=25kg) moves with a speed of 1.50ms-1 when 7.8m from the centre of a merry-go-round. Calculate
a) the cetripetal acceleraton of the child
b) th net horizontal force exerted on the child

Homework Equations


centripetal acceleration = v2/r
Fc=mv2/r

The Attempt at a Solution



centripetal acceleration = (150)2(squared)/7.8
=0.29m/s2

do i work out the horizontal force exerted on the child by using Fc=mv2/r?
25*(150)2(squared)/7.8 =7.21*10^4 N
 
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correct. Good job.
 
gee thanks for your time
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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