A 17 kg child descends a slide 3.5 m high and reaches the bottom with a speed of 4.5 m/s. How much work was done by friction as the child goes down the slide?
To calculate the work done by friction as the child goes down the slide, we need to apply the work-energy principle. The work done by friction can be determined by finding the difference between the initial and final energies of the child.
First, let's calculate the potential energy (PE) of the child at the top of the slide using the formula:
PE = m * g * h
Where:
m = mass of the child (17 kg)
g = acceleration due to gravity (approximately 9.8 m/s²)
h = height of the slide (3.5 m)
PE = 17 kg * 9.8 m/s² * 3.5 m
PE = 573.05 joules
Next, we need to calculate the final kinetic energy (KE) of the child at the bottom of the slide using the formula:
KE = 0.5 * m * v^2
Where:
m = mass of the child (17 kg)
v = velocity of the child at the bottom of the slide (4.5 m/s)
KE = 0.5 * 17 kg * (4.5 m/s)^2
KE = 170.625 joules
Now, we can find the work done by friction by taking the difference between the initial potential energy (PE) and the final kinetic energy (KE):
Work done by friction = PE - KE
Work done by friction = 573.05 joules - 170.625 joules
Work done by friction = 402.425 joules
Therefore, the work done by friction as the child goes down the slide is approximately 402.425 joules.