A proton traveling due west in a region that contains only a magnetic field experiences a vertically upward force (away from the
1 answer:
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Answer:
Explanation:
Let the minimum coefficient of static friction be .
Given:
Mass of the cylinder =
Radius of the cylinder =
Length of the cylinder =
Angle of inclination =
Initial velocity of the cylinder (Released from rest) = 0
Since, the cylinder is translating and rolling down the incline, it has both translational and rotational motion. So, we need to consider the effect of moment of Inertia also.
We know that, for a rolling object, torque acting on it is given as the product of moment of inertia and its angular acceleration. So,
Now, angular acceleration is given as:
Also, moment of inertia for a cylinder is given as:
Therefore, the torque acting on the cylinder can be rewritten as:
Consider the free body diagram of the cylinder on the incline. The forces acting along the incline are . The net force acting along the incline is given as:
Now, consider the forces acting perpendicular to the incline. As there is no motion in the perpendicular direction, net force is zero.
So,
Plugging in in equation (2), we get
Now, as per Newton's second law,
Now, torque acting on the cylinder is provided by the frictional force and is given as the product of frictional force and radius of the cylinder.
Therefore, the minimum coefficient of static friction needed for the cylinder to roll down without slipping is given as:
Answer:
Yes the frequency of the angular simple harmonic motion (SHM) of the balance wheel increases three times if the dimensions of the balance wheel reduced to one-third of original dimensions.
Explanation:
Considering the complete question attached in figure below.
Time period for balance wheel is:
m = mass of balance wheel
R = radius of balance wheel.
Angular frequency is related to Time period as:
As dimensions of new balance wheel are one-third of their original values
