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A small block can move in a straight horizontal line along AB. Flash lights from one side project its shadow on a vertical wall which has a horizontal cross-section as a circle. Find radial acceleration as a function of time.Read more on Sarthaks.com - https://www.sarthaks.com/1205316/small-block-can-move-straight-horizontal-line-along-flash-lights-from-one-side-project-its?
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A small block can move in a straight horizontal line along AB. Flash l...
Analysis:
The block moving along line AB will cast a shadow on the vertical wall. The cross-section of the wall is a circle, which means the shadow will move in a circular path as the block moves along AB.
Radial Acceleration:
- Radial acceleration is the component of acceleration directed towards the center of the circular path.
- It can be calculated using the formula: $a_r = \frac{v^2}{r}$, where $v$ is the velocity of the block and $r$ is the radius of the circular path.
Velocity of the Block:
- The velocity of the block can be expressed as: $v = \frac{ds}{dt}$, where $s$ is the distance traveled along line AB and $t$ is time.
Distance Traveled Along AB:
- The distance traveled by the block along line AB can be given as: $s = vt$.
Radius of the Circular Path:
- The radius of the circular path traced by the shadow on the wall is constant and equal to the radius of the circle cross-section of the wall.
Radial Acceleration as a Function of Time:
- Substituting the expressions for velocity and distance into the formula for radial acceleration, we get:
$a_r = \frac{(\frac{ds}{dt})^2}{r}$
$a_r = \frac{(\frac{d(vt)}{dt})^2}{r}$
$a_r = \frac{(v)^2}{r}$
$a_r = \frac{(\frac{ds}{dt})^2}{r}$
$a_r = \frac{(\frac{d(vt)}{dt})^2}{r}$
$a_r = \frac{(v)^2}{r}$
Therefore, the radial acceleration as a function of time is given by the formula: $a_r = \frac{v^2}{r}$.
The block moving along line AB will cast a shadow on the vertical wall. The cross-section of the wall is a circle, which means the shadow will move in a circular path as the block moves along AB.
Radial Acceleration:
- Radial acceleration is the component of acceleration directed towards the center of the circular path.
- It can be calculated using the formula: $a_r = \frac{v^2}{r}$, where $v$ is the velocity of the block and $r$ is the radius of the circular path.
Velocity of the Block:
- The velocity of the block can be expressed as: $v = \frac{ds}{dt}$, where $s$ is the distance traveled along line AB and $t$ is time.
Distance Traveled Along AB:
- The distance traveled by the block along line AB can be given as: $s = vt$.
Radius of the Circular Path:
- The radius of the circular path traced by the shadow on the wall is constant and equal to the radius of the circle cross-section of the wall.
Radial Acceleration as a Function of Time:
- Substituting the expressions for velocity and distance into the formula for radial acceleration, we get:
$a_r = \frac{(\frac{ds}{dt})^2}{r}$
$a_r = \frac{(\frac{d(vt)}{dt})^2}{r}$
$a_r = \frac{(v)^2}{r}$
$a_r = \frac{(\frac{ds}{dt})^2}{r}$
$a_r = \frac{(\frac{d(vt)}{dt})^2}{r}$
$a_r = \frac{(v)^2}{r}$
Therefore, the radial acceleration as a function of time is given by the formula: $a_r = \frac{v^2}{r}$.
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A small block can move in a straight horizontal line along AB. Flash lights from one side project its shadow on a vertical wall which has a horizontal cross-section as a circle. Find radial acceleration as a function of time.Read more on Sarthaks.com - https://www.sarthaks.com/1205316/small-block-can-move-straight-horizontal-line-along-flash-lights-from-one-side-project-its?
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