Solving Friction Question: Child on Stair Rail w/ 40 Degree Angle

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To determine the speed of a child sliding down a frictionless stair rail at a 40-degree angle, the relevant physics equation is f=ma, where the force acting on the child is due to gravity. The child has a mass of 25 kg and slides 4.0 m down the rail. The calculations initially attempted were incorrect, leading to a misunderstanding of the angle's sine value and its impact on acceleration. The correct approach involves using the gravitational force component along the incline to find the acceleration and then applying kinematic equations to find the final speed. The final speed at the bottom of the rail is calculated to be 7.1 m/s.
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Homework Statement



A child sits on a freshly oiled, straight stair rail that is frictionless. She has a mass of 25 kg and the rail makes a 40 degree angle with the ground. IF she slides 4.0 m before reaching the bottom, what is her speed there?

Homework Equations



f=ma

The Attempt at a Solution



I did .1(9.8)(sin30)
then i set it equal to .1a=.1(9.8)sin30
and got 4.9 m/s/s but the actual answer is 7.1 m/s/s?
where did i go wrong?
 
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Firstly, if it is frictionless then it is not a friction problem lol. What other equation do you think you need to solve this?
 
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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