a car moving on a road passes by kilometer 218 at 10:15 am and milestone 236 at 10:30 am. determine an average scalar speed in k
1 answer:
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Answer:
The distance travel by block before coming to rest is 0.122 m
Explanation:
Given:
Mass of block kg
Initial speed of block
Final speed of block
Coefficient of kinetic friction
Ramp inclined at angle 28.4°
Using conservation of energy,
Work done by frictional force is equal to change in energy,
Where
m
Therefore, the distance travel by block before coming to rest is 0.122 m
Answer:
I_{total} = 10 M R²
Explanation:
The concept of moment of inertia in rotational motion is equivalent to the concept of inertial mass for linear motion. The moment of inertia is defined
I = ∫ r² dm
For body with high symmetry it is tabulated, in these we can simulate them by a solid disk, with moment of inertia for an axis that stops at its center
I = ½ M R²
As you hear they ask for the moment of energy with respect to an axis parallel to the axis of the disk, we can use the theorem of parallel axes
I = + M D²
Where I_{cm} is the moment of inertia of the disk, M is the total mass of the system and D is the distance from the center of mass to the new axis
Let's apply these considerations to our problem
The moment of inertia of the four discs is
I_{cm} = I
I_{cm} = ½ M R²
For distance D, let's use the Pythagorean Theorem. As they indicate that the coins are touched the length of the square is L = 2R, the distance from any spine to the center of the block is
D² = (R² + R²)
D² = R² 2
Let's calculate the moment of inertia of a disk with respect to the axis that passes through the center of the square
I = ½ M R2 + M R² 2
I = 5/2 M R²
This is the moment of inertia of a disc as we have four discs and the moment of inertia is a scalar is additive, so
= 4 I
I_{total} = 4 5/2 M R²
I_{total} = 10 M R²