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.
PE at top-workdone=1/2 mv^2
I'm still confused. How does that equal 1/2mv2 and how does that solve the problem.
Starting potential energy less the work done on the way down equals the final kinetic energy.
From the final kinetic energy, you can compute the final velocity.
thank you, I got it
To find the child's speed at the bottom of the slide, we can use the principle of conservation of mechanical energy. This principle states that the total mechanical energy (potential energy + kinetic energy) in a system remains constant, assuming that there are no external nonconservative forces acting on the system.
In this case, the child starts at rest at the top of the slide, so their initial kinetic energy (KEi) is zero. The only form of energy they have is potential energy (PEi), given by mgh, where m is the mass of the child, g is the acceleration due to gravity, and h is the height of the slide.
PEi = mgh
At the bottom of the slide, the child has both potential energy (PEf) and kinetic energy (KEf). The potential energy is now zero, since the child is at ground level, and the kinetic energy is given by 1/2mv^2, where v is the child's speed at the bottom of the slide.
KEf = 1/2mv^2
According to the principle of conservation of mechanical energy, the initial mechanical energy should equal the final mechanical energy:
PEi + KEi = PEf + KEf
Since KEi is zero and PEi is mgh, we can simplify the equation to:
mgh = KEf
Now, we need to calculate the potential energy (PEf) that the child lost during the slide. This is given by the nonconservative work done on the child by the slide (Wnc). The nonconservative work is the negative of the work-energy theorem, given by Wnc = -ΔKE, where ΔKE is the change in kinetic energy.
Wnc = -ΔKE
-318 J = -KEf - KEi
-318 J = -KEf
Substitute the value of KEf into the equation:
-318 J = -1/2mv^2
Since the negative signs cancel out, we can simplify the equation to:
318 J = 1/2mv^2
Now we can solve for v by rearranging the equation:
v^2 = (2 * 318 J) / m
Finally, take the square root of both sides to get the value of v:
v = sqrt((2 * 318 J) / m)
Substituting the given values, m = 18.7 kg, we can calculate the value of v.