A water slide can be thought of as being frictionless. Let's say a slider starts from rest and goes down a slide that is 30 m long and is set at a 25 degree incline.
a) Determine the speed of the slider at the bottom of the slide.
b) Explain why you don't need to know the mass of the slider.
PE at top=KE at bottom
mgh=1/2 m v^2
mg30/sinTheta= 1/2 mv^2
solve for v.
sorry, what's mg?
mg is mass * acceleration due to gravity, mg is weight.
so i won't have a numerical answer?
yes,notice m divides out. You have to put the values of g and SinTheta to get the answer. I don't serve on silver platters (just blueplate).
To determine the speed of the slider at the bottom of the slide, we can use the principles of conservation of energy. The potential energy at the top of the slide will be converted to kinetic energy at the bottom of the slide.
a) First, we need to calculate the potential energy at the top of the slide. The potential energy can be determined using the formula:
Potential Energy = mass * gravity * height
Since the height is not provided, we can calculate it using the given information. The incline forms a right-angled triangle with the vertical height and the horizontal length of the slide. We can use trigonometry to find the height.
Height = Length * sin(angle)
Height = 30 m * sin(25 degrees)
Now that we have the height, we can proceed to calculate the potential energy:
Potential Energy = mass * 9.8 m/s^2 * Height
b) Now, here's why we don't need to know the mass of the slider. If we look at the expression for potential energy, we notice that the mass of the object does not appear in the equation. This means that the mass of the slider does not affect the potential energy or the speed at the bottom of the slide.
The conversion from potential energy to kinetic energy is solely dependent on the height and the force of gravity, not the mass. Therefore, regardless of the mass, the potential energy will be fully converted into kinetic energy.
Considering the conservation of energy, we can equate the potential energy to the kinetic energy at the bottom of the slide:
Potential Energy = Kinetic Energy
As the potential energy is converted to kinetic energy, we can write:
mass * 9.8 m/s^2 * Height = 1/2 * mass * velocity^2
Now, we can cancel out the mass from both sides of the equation:
9.8 m/s^2 * Height = 1/2 * velocity^2
Finally, we solve for the velocity:
velocity = sqrt(2 * 9.8 m/s^2 * Height)
Plugging in the known values, we can calculate the speed of the slider at the bottom of the slide.