(i)For the wheel of diameter 10 cm, find its final speed after traversing a distance of 10 m down an incline of 25º. Assume it starts from rest.
I know i have to use the conservation of energy but how?
i don't understand where to start off
loss of GPE= gainoflinearKE+gainrotationalKE
You are going to have to decide if the wheel is a hoop, or a solid disk to find the moment of inertia.
Remember, for each 2PI radians of rotation, the wheel moves linearly 2PIr distance.
if w is the angular speed, then rw is the linear velocity.
g*m*10cos25=1/2 I w^2+1/2 M(rw)^
and once you decide solid wheel or hoop, you fill in for I, and then solve for w.
Wow thanks very much
I was usig the wrong formula for loss of PE that's where i went wrong its always helpful to have people to tell you where youve gone wrong
To find the final speed of the wheel after traversing a distance down an incline, you can use the principle of conservation of energy. This principle states that the total mechanical energy (sum of kinetic and potential energy) of a system remains constant, assuming no external forces or nonconservative forces are acting on it.
To start off, let's break down the problem into smaller steps:
Step 1: Calculate the potential energy at the starting position.
The potential energy (PE) of an object is given by the formula PE = m * g * h, where m is the mass of the object, g is the acceleration due to gravity, and h is the vertical distance or height.
In this case, since we know the diameter of the wheel (10 cm), we can calculate the mass (m) assuming a uniform density. The formula to calculate the mass of a wheel is m = π * r^2 * h * ρ, where r is the radius of the wheel, h is the thickness of the wheel, and ρ is the density of the material (which we'll assume to be constant). Note that the thickness of the wheel is required because we need the volume of the wheel.
Step 2: Calculate the potential energy at the final position.
Since the wheel is moving down an incline, it will lose potential energy and convert it into kinetic energy. The kinetic energy (KE) is given by the formula KE = (1/2) * m * v^2, where v is the final velocity or speed of the wheel.
Step 3: Set up the conservation of energy equation.
According to the conservation of energy principle, the total mechanical energy at the starting position (PE) is equal to the total mechanical energy at the final position (KE). Mathematically, this can be expressed as PE = KE.
Step 4: Solve for the final velocity (v).
Rearranging the equation PE = KE, we can substitute the expressions for PE and KE from Steps 1 and 2, respectively. Once you plug in the values, you can solve for the final velocity (v).
Note: To convert angles from degrees to radians, you can use the formula radians = degrees * (π/180).
By following these steps, you can use the conservation of energy to find the final speed of the wheel after traversing the given distance down the incline.