(13%) Problem 8: A child of mass m = 29 kg slides down a slide of height h = 2.8

Question

(13%) Problem 8: A child of mass m = 29 kg slides down a slide of height h = 2.8 m without friction. Let gravitational potential energy be zero at ground level Randomized Variables m-29 kg h 2.8 m 33% Part (a) Write an expression for the child's total mechanical energy, E, at the top of the slide Grade Summary Deductions Potential 0% 100% 789 Submissions Attempts remaining: 3 % per attempt) detailed view 123 0 BACKSPACE Submit Hint I give up! Hints: 3% deduction per hint. Hints remaining: 3 Feedback: 5% deduction per feedback. 33% Part b) Calculate the change in the child's potential energy, U in Joules, from the top to the bottom of the slide at ground level (ie AU-Uground- Usop 33% Part (c) What is the child's final speed, vfin m/s?

Explanation / Answer

Part (a) -

Child's total mechanical energy at the top of the slide = Potential energy of the child = m*g*h

Part (b) -

The surface is frictionless.

So, the total mechanical energy at the ground = kinetic energy of the child = (1/2)*m*v^2

=> Uground = (1/2)*m*v^2

This is equal to the potential energy at the top, Utop.

So, delta U = Uground - Utop = 0

Part (c) -

By energy conservation -

m*g*h = (1/2)*m*v^2

=> v^2 = 2*g*h

=> v = sqrt[2*g*h] = sqrt[2*9.81*2.8] = 7.41 m/s

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