A 35.7 kg child starting from restslides down a water slide with a vertical heig

Question

A 35.7 kg child starting from restslides down a water slide with a vertical height of 19.3 m. (Neglect friction.) (a) What is the child's speed halfway down theslide's vertical distance?
m/s
(b) What is the child's speed three-quarters of the way down?
m/s A sled and rider with a combined weight of45 kg are at rest on the top of a hill14 m high. (a) What is their total energy at the top ofthe hill?
J
(b) Assuming there is no friction, what is the total energy onsliding halfway down the hill?
J

(a) What is the child's speed halfway down theslide's vertical distance?
m/s
(b) What is the child's speed three-quarters of the way down?
m/s A sled and rider with a combined weight of45 kg are at rest on the top of a hill14 m high. (a) What is their total energy at the top ofthe hill?
J
(b) Assuming there is no friction, what is the total energy onsliding halfway down the hill?
J
(a) What is their total energy at the top ofthe hill?
J
(b) Assuming there is no friction, what is the total energy onsliding halfway down the hill?
J

Explanation / Answer

Easiest way to do this problem is by conservation of energy. Difference in PE between child at top and child at bottom is PE=mg(y) (y is vertical position) = 35.7*9.8*19.3 =whatever. Energy is conserved (main loss of energy from child would be byfriction and we're told to neglect it) so total energy is always aconstant. It's easy to work out the total energy when the child is at the topof the slide b/c its not moving so KE=0: E_tot=PE+KE=35.7*9.8*19.3+0 Now, halfway down the hill, the height of the child is now 19.3/2compared to the bottom so clearly the child's PE is reduced to35.7*9.8*19.3/2. Energy is conserved so that missing PE is nowKE: KE=E_tot-PE=35.7*9.8*19.3-35.7*9.8*19.3/2=35.7*9.8*19.3/2 (whateverthat is). and you can work out the speed b/c KE=1/2 mv^2 rearrange with v the subject: v=sqrt(2 KE/m). 3/4 of the way down the hill, the child's height wrt the bottom is19.3/4. So go through the same steps: work out the PE, then the KE. Finallyuse KE to work out the speed. The sled and rider question is done in just the same way. Easiest way to find total E is when either KE or PE is 0, in thiscase again KE=0 when they are at the top of the hill (they aren'tmoving). So E_tot=PE(at top of hill). Then it's all more of the same. Hope this helps.

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