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?
change in potential energy = m g h = 17*9.81*3.5
= 584 Joules
Kinetic energy = (1/2)17 (4.5)^2
= 172 Joules
The difference was lost to friction on the way down
584 - 172 = 412 Joules
Well, let me slide into this question with a witty answer for you! The work done by friction can be calculated using the formula: work = force × distance. Since the slide is as smooth as a baby's bottom, there is no friction involved. So, the work done by friction is about as much work as I put into avoiding my responsibilities, which is none at all!
To determine the work done by friction as the child goes down the slide, we need to first calculate the gravitational potential energy at the top of the slide and then subtract the kinetic energy at the bottom of the slide.
The gravitational potential energy (PE) at the top of the slide can be calculated using the formula: PE = m * g * h, where m is the mass of the child (17 kg), g is the gravitational acceleration (9.8 m/s^2), and h is the height of the slide (3.5 m).
PE = (17 kg) * (9.8 m/s^2) * (3.5 m)
PE = 582.05 J (Joules)
The kinetic energy (KE) at the bottom of the slide can be calculated using the formula: KE = 0.5 * m * v^2, where m is the mass of the child (17 kg) and v is the speed at the bottom of the slide (4.5 m/s).
KE = 0.5 * (17 kg) * (4.5 m/s)^2
KE = 170.775 J
Now, we can determine the work done by friction by subtracting the kinetic energy from the gravitational potential energy:
Work done by friction = PE - KE
Work done by friction = 582.05 J - 170.775 J
Work done by friction = 411.275 J
Therefore, the work done by friction as the child goes down the slide is 411.275 Joules.
To find the amount of work done by friction as the child goes down the slide, we can use the work-energy principle. The work-energy principle states that the work done on an object is equal to the change in its kinetic energy.
First, let's find the initial kinetic energy of the child at the top of the slide. Kinetic energy (KE) is given by the equation: KE = 0.5 * mass * velocity^2.
Given:
Mass of the child (m) = 17 kg
Initial velocity at the top of the slide (vi) = 0 m/s (since the child starts from rest)
Using the formula:
KE_initial = 0.5 * m * vi^2
KE_initial = 0.5 * 17 kg * (0 m/s)^2
KE_initial = 0 J
The initial kinetic energy of the child is 0 J since the child starts from rest.
Next, let's find the final kinetic energy of the child at the bottom of the slide. Given:
Final velocity at the bottom of the slide (vf) = 4.5 m/s
Using the formula for kinetic energy:
KE_final = 0.5 * m * vf^2
KE_final = 0.5 * 17 kg * (4.5 m/s)^2
KE_final = 68.85 J
The final kinetic energy of the child at the bottom of the slide is 68.85 J.
Since the child is losing energy due to friction, the work done by friction is equal to the change in kinetic energy:
Work = KE_final - KE_initial
Work = 68.85 J - 0 J
Work = 68.85 J
Therefore, the work done by friction as the child goes down the slide is 68.85 J.