Work Done by Skier on Ski Slope: Calculate & Find Speed

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The skier, with a mass of 70 kg, ascends a slope 20 m high, resulting in a work done against gravity calculated as 1400 J (Work Done = F x D). The confusion arises regarding whether to multiply this work by the gravitational force (10 N/kg) for further calculations. For the next part, the potential energy change (PE = mgh) should equal the kinetic energy (KE = 1/2 mv^2) to find the skier's speed at the bottom. The skier's weight is crucial in determining the forces involved, but the initial work done does not need to be multiplied by gravity again. The calculations should focus on the relationship between potential and kinetic energy without additional multiplication by gravity.
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Homework Statement


A skier with a mass of 70kg rides a chairlift to a point of 20m higher up a ski slope.
She then Skis back down to the bottom of the chairlift.

Calculate the work done against gravity by the chairlift in carrying the skier up the slope
(Assume that g=10n/kg)

Homework Equations


Work Done = F x D


The Attempt at a Solution


Work done = 70 x 20
= 1400

*This is the part where I am confused.*

When we started out doing Work done, we never involved work done against another force. So Would I multiply the Work Done (1400) by 10 (kg, Gravity)?

Thanks,
Phykid

Edit - The following question: "Find the skier's speed when she reaches the bottom of the chairlift.
Ignore the effects of friction and air resistance and assume that g=10n/kg
 
Last edited:
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Rememebr the force is the weight of the skier in Newtons, F = m g

To get the speed simply assume that potential energy change PE = m g h
equals the kinetic energy KE = 1/2 m v^2
 
So if I am working it out against gravity, would I multiply the 14000 by 10 (gravity)?

Thanks.
Phykid
 
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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