Rotational Dynamics Problem!

A uniform bar AB 10 m long and weighing 280 N is hinged at B and rests upon a 400 N block as shown. If the coefficient of friction at all contact surfaces is 0.4. The value of horizontal force F required to start the motion of the 400 N block is...?

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Note by Siddharth Iyer
6 years, 1 month ago

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2 votes

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272 N .

jatin yadav - 6 years, 1 month ago

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I am sorry but the correct answer is 320 N. Could you tell me how you approached the problem???

Siddharth Iyer - 6 years, 1 month ago

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Ok i got my mistake , i was not considering torque due to friction on the rod.

Draw proper FBD. Let N1N_{1} and N2N_{2} be the normal reactions between rod and block and between ground block respectively. Let f1f_{1} and f2f_{2} be corresponding frictions.

At the verge of slipping , f1=0.4N1,f2=0.4N2f_{1} = 0.4N_{1} , f_{2} = 0.4N_{2}

On the rod , we can balance torque apout the hinge.

Anticlockwise torque due to friction and weight = clockwise torque due to normal reaction.

mglsinθ2+0.4N1lcosθ=N1lsinθ\Rightarrow \frac{mglsin\theta}{2} + 0.4N_{1}lcos\theta = N_{1}lsin\theta ,

N1=200N\Rightarrow N_{1} = 200N

Analysing FBD of block ,

N2=Wblock+N1=600NN_{2} = W_{block} + N_{1} = 600N

Ff1+f2=0.4(N1+N2) F \geq f_{1} + f_{2} = 0.4(N_{1} + N_{2}) = 0.4×800=320N0.4 \times 800 = \fbox{320N}

jatin yadav - 6 years, 1 month ago

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@Jatin Yadav Thanks!!! I figured my mistake too. i was not considering torque due to normal reaction.

Siddharth Iyer - 6 years, 1 month ago

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@Jatin Yadav But when I solved the torque equation, I got N1N_1 as 300N. Can you check why?

Rohan Rao - 6 years, 1 month ago

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@Rohan Rao Sorry , i can't check without your equations.

jatin yadav - 6 years, 1 month ago

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@Jatin Yadav No sorry never mind, I got it.

Rohan Rao - 6 years, 1 month ago

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A uniform bar AB 10 m long and weighing 280 N is hinged at B and rests upon a 400 N block as shown. If the coefficient of friction at all contact surfaces is 0.4. The value of horizontal force F required to start the motion of the 400 N block is...? what is the solution

naveen kumar - 1 year, 10 months ago

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