Physics: Find Wagon Speed Up 18.1° Hill Given Tension and Distance

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To find the speed of a 32.1 kg wagon towed up an 18.1° incline with a tension of 114 N, the problem involves calculating the net force acting on the wagon and applying Newton's second law. The gravitational force component acting down the incline must be subtracted from the tension to determine the net force. Using this net force, the acceleration can be calculated, and then the final speed after moving 62.5 m can be determined using kinematic equations. The solution requires neglecting friction and starting from rest. The final speed of the wagon can be expressed in meters per second (m/s).
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A 32,1 kg wagon is towed up a hill inclined at 18.1 degrees with respect to the horizontal. The two rope is parallel to the incline and has a tension of 114N in it. Assume that the wagon starts from rest at the bottom of the hill and neglet friction. The acceleration of gravity is 9.8m/s2. How fast is the wagin going after moving 62.5m up the hill? Answer in units of m/s:cry:
 
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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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