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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 in form of (vR) / ( 2 R t − v t ² )?
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A small block can move in a straight horizontal line along AB. Flash l...
Radial Acceleration Calculation
- The shadow of the moving block on the circular cross-section wall creates an arc.
- The radial acceleration can be calculated by analyzing the motion of the shadow.
- Let the block move with velocity v and the shadow move with velocity vR.
- The radius of the circle is R and the time taken is t.
Relationship between velocities
- The relationship between the velocities of the block and its shadow can be expressed as: vR = R * dθ/dt.
- Here, dθ is the angular displacement of the shadow on the circle.
Calculating radial acceleration
- Radial acceleration (aR) is given by aR = vR^2 / R.
- Substituting the value of vR from the relationship between velocities, we get aR = (R * dθ/dt)^2 / R.
- Simplifying further, aR = R * (dθ/dt)^2.
- As we know, dθ/dt = v / R (angular velocity), substituting this value, we get aR = R * (v/R)^2.
- Therefore, aR = v^2 / R.
Expressing as a function of time
- To express the radial acceleration as a function of time, we need to relate the velocity of the block with time.
- Given that the block moves along AB in a straight line, the velocity of the block can be expressed as v = (2Rt - vt^2).
- Substituting this value in the expression for radial acceleration, we get aR = [(2Rt - vt^2)^2] / R.
- Simplifying further, aR = (4R^2t^2 - 4Rvt^3 + v^2t^4) / R.
- Finally, aR = 4Rt^2 - 4vt^3 + v^2t^4.
Therefore, the radial acceleration as a function of time is (vR) / (2Rt - vt^2), where vR is the velocity of the shadow and v is the velocity of the block.
- The shadow of the moving block on the circular cross-section wall creates an arc.
- The radial acceleration can be calculated by analyzing the motion of the shadow.
- Let the block move with velocity v and the shadow move with velocity vR.
- The radius of the circle is R and the time taken is t.
Relationship between velocities
- The relationship between the velocities of the block and its shadow can be expressed as: vR = R * dθ/dt.
- Here, dθ is the angular displacement of the shadow on the circle.
Calculating radial acceleration
- Radial acceleration (aR) is given by aR = vR^2 / R.
- Substituting the value of vR from the relationship between velocities, we get aR = (R * dθ/dt)^2 / R.
- Simplifying further, aR = R * (dθ/dt)^2.
- As we know, dθ/dt = v / R (angular velocity), substituting this value, we get aR = R * (v/R)^2.
- Therefore, aR = v^2 / R.
Expressing as a function of time
- To express the radial acceleration as a function of time, we need to relate the velocity of the block with time.
- Given that the block moves along AB in a straight line, the velocity of the block can be expressed as v = (2Rt - vt^2).
- Substituting this value in the expression for radial acceleration, we get aR = [(2Rt - vt^2)^2] / R.
- Simplifying further, aR = (4R^2t^2 - 4Rvt^3 + v^2t^4) / R.
- Finally, aR = 4Rt^2 - 4vt^3 + v^2t^4.
Therefore, the radial acceleration as a function of time is (vR) / (2Rt - vt^2), where vR is the velocity of the shadow and v is the velocity of the block.
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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 in form of (vR) / ( 2 R t − v t ² )?
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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 in form of (vR) / ( 2 R t − v t ² )? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about 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 in form of (vR) / ( 2 R t − v t ² )? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 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 in form of (vR) / ( 2 R t − v t ² )?.
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 in form of (vR) / ( 2 R t − v t ² )? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about 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 in form of (vR) / ( 2 R t − v t ² )? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 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 in form of (vR) / ( 2 R t − v t ² )?.
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