At a playground, a 18.7 kg child plays on a slide that drops through a height of 2.07 m. The child starts at rest at the top of the slide. On the way down, the slide does a nonconservative work of -318 J on the child. What is the child's speed at the bottom of the slide?
I have used v = sgrt 2gh and 1/2mv2 but to no avail.
I HAVE THE ANSWER. THANK YOU
To find the child's speed at the bottom of the slide, we need to consider the energy transformations happening during the child's descent.
First, let's calculate the gravitational potential energy (GPE) that is converted to kinetic energy (KE) as the child slides down the slide. The equation relating GPE and KE is:
GPE = KE
The gravitational potential energy is given by the equation:
GPE = m * g * h
where m is the mass of the child (18.7 kg), g is the acceleration due to gravity (9.8 m/s^2), and h is the height of the slide (2.07 m). Plugging in the values, we have:
GPE = 18.7 kg * 9.8 m/s^2 * 2.07 m
Next, we know that the slide does a nonconservative work of -318 J on the child. This work is associated with friction and other non-conservative forces that act against the child's motion. According to the work-energy principle, the net work done on an object is equal to the change in its kinetic energy:
Work = KE_final - KE_initial
Since the child starts at rest at the top of the slide, their initial kinetic energy (KE_initial) is zero. Therefore, we can rewrite the equation as:
Work = KE_final - 0
which simplifies to:
Work = KE_final
Now we have two equations:
GPE = KE_final
Work = KE_final
We can set these two equations equal to each other:
GPE = Work
Plugging in the calculated values, we have:
18.7 kg * 9.8 m/s^2 * 2.07 m = -318 J
Solving this equation will give us the height at which the child will come to rest at the bottom of the slide.