The normal reaction ‘N’ for a vehicle of 800kg mass, negotiating a turn on a 30° banked road at maximum possible speed without skidding is_________× 10³ kg m/s².

[Given cos30° = 0.87, $μ_{5} = 0.2]$

Option 1 -

6.96

Option 2 -

10.2

Option 3 -

12.4

Option 4 -

7.2

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1 Answer

Answered by

alok kumar singh | Contributor-Level 10

a month ago

Correct Option - 2

Detailed Solution:

In the frame of vehicle, vehicle is in equilibrium under the influence of pseudo force F_P

$F_{P} = \frac{m v^{2}}{R}$

N = mg cos 30° + F_P sin 30°

$\Rightarrow N = m g c o s 30 ° + \frac{m v^{2}}{R} s i n 30 ° . (i)$

, and

$f_{S} = \frac{m v^{2}}{R} c o s 30 ° - m g s i n 30 °$

By doing (1) × cos 30° - (2) × sin 30°, we have

$\Rightarrow N = \frac{800 \times 10}{0.87 - 0.2 \times 0.5} = \frac{800 \times 10}{0.77} = 10.2 \times 1 0^{3} k g m / s^{2}$

In the frame of vehicle, vehicle is in equilibrium under the influence of pseudo force FP  <math> <mrow> <msub> <mrow> <mi>F</mi> </mrow> <mrow> <mi>P</mi> </mrow> </msub> <mo>=</mo> <mfrac> <mrow> <mi>m</mi> <msup> <mrow> <mi>v</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msup> </mrow> <mrow> <mi>R</mi> </mrow> </mfrac> </mrow> </math>            <!- [if gte mso 9]><xml> <o:OLEObject Type="Embed" ProgID="Equation.DSMT4" ShapeID="_x0000_i1025" DrawAspect="Content" ObjectID="_1816092514"> </o:OLEObject></xml><! [endif]->N = mg cos 30° + FP sin 30° <math> <mrow> <mo>⇒</mo> <mi>N</mi> <mo>=</mo> <mi>m</mi> <mi>g</mi> <mi>c</mi> <mi>o</mi> <mi>s</mi> <mn>3</mn> <mn>0</mn> <mo>°</mo> <mo>+</mo> <mfrac> <mrow> <mi>m</mi> <msup> <mrow> <mi>v</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msup> </mrow> <mrow> <mi>R</mi> </mrow> </mfrac> <mi>s</mi> <mi>i</mi> <mi>n</mi> <mn>3</mn> <mn>0</mn> <mo>°</mo> <mo>.</mo> <mrow> <mo> (</mo> <mrow> <mi>i</mi> </mrow> <mo>)</mo> </mrow> </mrow> </math>              <!- [if gte mso 9]><xml> <o:OLEObject Type="Embed" ProgID="Equation.DSMT4" ShapeID="_x0000_i1026" DrawAspect="Content" ObjectID="_1816092515"> </o:OLEObject></xml><! [endif]->, and <math> <mrow> <msub> <mrow> <mi>f</mi> </mrow> <mrow> <mi>S</mi> </mrow> </msub> <mo>=</mo> <mfrac> <mrow> <mi>m</mi> <msup> <mrow> <mi>v</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msup> </mrow> <mrow> <mi>R</mi> </mrow> </mfrac> <mi>c</mi> <mi>o</mi> <mi>s</mi> <mn>3</mn> <mn>0</mn> <mo>°</mo> <mo>−</mo> <mi>m</mi> <mi>g</mi> <mi>s</mi> <mi>i</mi> <mi>n</mi> <mn>3</mn> <mn>0</mn> <mo>°</mo> </mrow> </math>              <!- [if gte mso 9]><xml> <o:OLEObject Type="Embed" ProgID="Equation.DSMT4" ShapeID="_x0000_i1027" DrawAspect="Content" ObjectID="_1816092516"> </o:OLEObject></xml><! [endif]->By doing (1) × cos 30° - (2) × sin 30°, we have <math> <mrow> <mo>⇒</mo> <mi>N</mi> <mo>=</mo> <mfrac> <mrow> <mn>8</mn> <mn>0</mn> <mn>0</mn> <mo>×</mo> <mn>1</mn> <mn>0</mn> </mrow> <mrow> <mn>0</mn> <mo>.</mo> <mn>8</mn> <mn>7</mn> <mo>−</mo> <mn>0</mn> <mo>.</mo> <mn>2</mn> <mo>×</mo> <mn>0</mn> <mo>.</mo> <mn>5</mn> </mrow> </mfrac> <mo>=</mo> <mfrac> <mrow> <mn>8</mn> <mn>0</mn> <mn>0</mn> <mo>×</mo> <mn>1</mn> <mn>0</mn> </mrow> <mrow> <mn>0</mn> <mo>.</mo> <mn>7</mn> <mn>7</mn> </mrow> </mfrac> <mo>=</mo> <mn>1</mn> <mn>0</mn> <mo>.</mo> <mn>2</mn> <mo>×</mo> <mn>1</mn> <msup> <mrow> <mn>0</mn> </mrow> <mrow> <mn>3</mn> </mrow> </msup> <mi>k</mi> <mi>g</mi> <mi>m</mi> <mo>/</mo> <msup> <mrow> <mi>s</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msup> </mrow> </math> <!- [if gte mso 9]><xml> <o:OLEObject Type="Embed" ProgID="Equation.DSMT4" ShapeID="_x0000_i1025" DrawAspect="Content" ObjectID="_1816092564"> </o:OLEObject></xml><! [endif]->

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The normal reaction ‘N’ for a vehicle of 800kg mass, negotiating a turn on a 30° banked road at maximum possible speed without skidding is_________× 10³ kg m/s².

[Given cos30° = 0.87, $μ_{5} = 0.2]$

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The normal reaction ‘N’ for a vehicle of 800kg mass, negotiating a turn on a 30° banked road at maximum possible speed without skidding is_________× 103 kg m/s2. [Given cos30° = 0.87, μ 5 = 0 . 2 ]

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The normal reaction ‘N’ for a vehicle of 800kg mass, negotiating a turn on a 30° banked road at maximum possible speed without skidding is_________× 10³ kg m/s².

[Given cos30° = 0.87, $μ_{5} = 0.2]$