Respuesta :
Answer: both hoops have the same kinetic energy at the bottom of the incline.
Explanation:
If we assume no work done by non conservative forces (like friction) , the total mechanical energy must be conserved.
K1 + U1 = K2 + U2
If both hoops start from rest, and we choose the bottom of the incline to be the the zero reference level for gravitational potential energy, then
K1 = 0 and U2 = 0
⇒ ΔK = ΔU = m g. h
If both inclines have the same height, and both hoops have the same mass m, the change in kinetic energy, must be the same for both hoops.
The both the hoops have the same amount of total kinetic energy (transitional and rotational) at the bottom of the incline.
What is kinetic energy?
Kinetic energy is a type of energy, which a body is posses due to its motion. The kinetic energy of a body can be found with the following formula,
[tex]KE=\dfrac{1}{2}mv^2[/tex]
Here, (m) is the mass of the body, and (v) is the speed of the body.
For the conservation of energy, the sum of initial kinetic energy and the potential energy of the system is equal to the sum of final kinetic energy and the potential energy of the system. It can be given as,
[tex]K_i+U_i=K_f+U_f[/tex]
Here, (K) represent the kinetic energy and (U) represent the potential energy of the system.
Two hoops, starting from rest, roll down identical inclined planes. Therefore, the initial kinetic energy is zero and for the bottom of the slide, the final potential energy is zero. Therefore, by above law,
[tex]\Delta K=\Delta U[/tex]
Both have the same mass M, but, one hoop has twice the radius of the other.
Hoop 1 Radius = R and Mass = M
Hoop 2 Radius = 1/2 R and Mass = M
The moment of inertia for each hoop is I = Mr², where r is the radius. The potential energy of the hoops is the product of mass, gravitational force and height. Thus, from the above expression,
[tex]\Delta K=\Delta U\\\Delta K=Mgh[/tex]
Both the hoops have same mass, and height. Thus from above equation, it is cleared that they have same kinetic energy.
Thus, the both the hoops have the same amount of total kinetic energy (transitional and rotational) at the bottom of the incline.
Learn more about the kinetic energy here;
https://brainly.com/question/25959744
