What are two main types of friction
2 answers:
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Answer:
vcyl / vsph = 1.05
Explanation:
- The kinetic energy of a rolling object can be expressed as the sum of a translational kinetic energy plus a rotational kinetic energy.
- The traslational part can be written as follows:
- The rotational part can be expressed as follows:
- where I = moment of Inertia regarding the axis of rotation.
- ω = angular speed of the rotating object.
- If the object has a radius R, and it rolls without slipping, there is a fixed relationship between the linear and angular speed, as follows:
- For a solid cylinder, I = M*R²/2 (4)
- Replacing (3) and (4) in (2), we get:
- Adding (5) and (1), we get the total kinetic energy for the solid cylinder, as follows:
- Repeating the same steps for the spherical shell:
- Since we know that both masses are equal each other, we can simplify (6) and (9), cancelling both masses out.
- And since we also know that both objects have the same kinetic energy, this means that (6) are (9) are equal each other.
- Rearranging, and taking square roots on both sides, we get:
- This means that the solid cylinder is 5% faster than the spherical shell, which is due to the larger moment of inertia for the shell.
at the lowest point in the trajector, the kinetic energy of the bob is 300 J.
Explanation:
The total mechanical energy of the bob at any point of its motion is given by
Where
is the kinetic energy, where
m is the mass of the bob
v is its speed
is the gravitational potential energy, where
g is the acceleration of gravity
h is the height of the bob, measured with respect to the lowest point of the trajector
In absence of friction, the total mechanical energy E remains constant. So we have:
- When the bob swings upward, the PE increases (because h increases) and the KE decreases (so the speed decreases). At the highest point in the trajector, the speed of the bob is zero (v=0), so its KE is also zero and all the mechanical energy is potential energy: U = 300 J
- When the bob swings downward, the PE decreases (because h decreases) and the KE increases (so the speed increases). At the lowest point in the trajectory, the height has become zero (h=0), so the PE is zero and all the mechanical energy is kinetic energy: KE = 300 J
Therefore, at the lowest point in the trajector, the kinetic energy of the bob is 300 J.
Learn more about kinetic energy:
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