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a car travelling at 50m/h on a horizontal highway (a) if the coefficient of static friction between road and tyres on a rainy da
y is 0.100, what is the minimum distance in which the car will stop?
1 answer:
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Answer:
the equivalent mass :
the equation of the motion of the block of mass in terms of its displacement is =
Explanation:
Let use m₁ to represent the mass of the block and m₂ to represent the mass of the cylinder
The radius of the cylinder be = R
The distance between the center of the pulley to center of the block to be = x
Also, the angles of inclinations of the cylinder and the block with respect to the ground to be and
respectively.
The velocity of the block to be = v
The equivalent mass of the system =
In the terms of the equivalent mass, the kinetic energy of the system can be written as:
--------------- equation (1)
The angular velocity of the cylinder = : &
The inertia of the cylinder about its center to be = I
The angular velocity of the cylinder can be written as:
The kinetic energy of the system in terms of individual mass can be written as:
By replacing with
; we have:
------------------ equation (2)
Equating both equation (1) and (2); we have:
Therefore, the equivalent mass : which is read as;
The equivalent mass is equal to the mass of the block plus the mass of the cylinder plus the inertia by the square of the radius.
The expression for the force acting on equivalent mass due to the block is as follows:
Also; The expression for the force acting on equivalent mass due to the cylinder is as follows:
Equating the above both equations; we have the equation of motion of the equivalent system to be
which can be written as follows from the previous derivations
Finally; the equation of the motion of the block of mass in terms of its displacement is =
For a photographer that wishes to determine the color of light that he can use in a dark room that will not expose the films he is processing, having used a Blue Incandescent bulb, he should proceed to use a Red Incandescent bulb for the next trial.
The photographer in question is performing an experiment. For these kinds of experiments it is important to identify the variables present, which can be of three kinds:
- Control variables
- Dependent variables
- Independent variables
For this experiment, the dependent variable is the exposure of the light onto the films, given that this is what we wish to measure. The independent variable will be the color of the light being used which is what will affect the dependent variable.
The remaining variable must be the control variable. Unlike the previous variables, we can have more than one of these. The control variable is there to make sure that only the dependent variable is affecting the outcome. We do this by keeping the control variable the same through each trial, which is why the photographer should not change the type of bulb in the second experiment, changing only the color of the light.
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