A child who has a mass of 17 kg slides down a slide from a height of 3.3 m. If friction does a non-conservative work of -143 J, what is the speed (in m/s) of the child at the bottom of the slide? The acceleration due to gravity is 9.81 m/s2
final KE= initialPE-frictionenergy
1/2 m vf^2=m g 3.3 - 143
calculate vf
To find the speed of the child at the bottom of the slide, we can use the principle of conservation of mechanical energy. This principle states that the total mechanical energy of an object remains constant if only conservative forces (like gravity) are acting on it and no energy is lost due to non-conservative forces (like friction).
The total mechanical energy of an object is the sum of its potential energy and kinetic energy. At the top of the slide, the child only has potential energy, which is given by the formula:
Potential energy = mass * gravity * height
So, the potential energy of the child at the top of the slide is:
Potential energy = 17 kg * 9.81 m/s² * 3.3 m
Next, we need to consider the non-conservative work done by friction. The work done by friction is equal to the change in mechanical energy of the child:
Work done by friction = Change in mechanical energy
Since the work done by friction is given as -143 J, we can write:
-143 J = Change in mechanical energy
Finally, at the bottom of the slide, all the potential energy is converted into kinetic energy. The kinetic energy of the child is given by the formula:
Kinetic energy = 0.5 * mass * speed²
Since there are no other forces acting on the child except for gravity and friction, we can equate the potential energy at the top of the slide to the kinetic energy at the bottom:
Potential energy = Kinetic energy
Now we can set up the equation:
mass * gravity * height = 0.5 * mass * speed²
Simplifying this equation, we get:
9.81 m/s² * 3.3 m = 0.5 * speed²
Solving for speed, we get:
Speed = √[(9.81 m/s² * 3.3 m * 2) / mass]
Plugging in the given mass of 17 kg into the equation, we can calculate the speed of the child at the bottom of the slide.