In the figure shown, all surfaces are smooth and block A and wedge B have mass 10 kg and 20 kg respectively. Find the sum of normal reaction between block A and B, spring force and normal reaction of ground on block B.If the whole system is in equilibrium.
Take g= 1 0 m / s 2
Sin(37)=3/5
It is not an original problem .
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@Steven Chase very nice solution.
@Steven Chase ,i have updated the question,thanks!
Btw nice solution.
Thanks for updating the problem statement by specifying that the system is in equilibrium.
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It would be good to specify in the problem statement to take sin ( 3 7 ∘ ) = 0 . 6 as doing so will give the exact integer answer. In reality, sin ( 3 7 ∘ ) = 0 . 6
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@Karan Chatrath
You were talking that, and now??
Isn't it a contradiction?
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@Talulah Riley – I'm sorry, I don't understand what you are saying
Because you have given an integer answer, you have to give the values of sin 3 7 ° and cos 3 7 ° as 5 3 and 5 4 respectively.
(1) Normal reaction force between the block and the wedge is 1 0 g cos 3 7 ° = 8 0 N
(2) Spring force is 1 0 g sin 3 7 ° cos 3 7 ° = 4 8 N
(3) Normal reaction of ground on the wedge is 2 0 g + 1 0 g cos 2 3 7 ° = 2 6 4 N
Therefore their sum is 8 0 + 4 8 + 2 6 4 = 3 9 2 N.
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There are a few problems here, given that the requested answer is in integer format. First, it needs to be stated that the gravitational acceleration is 1 0 . And then, the answer is not actually an integer, so it needs to be stated to round to the nearest whole number.
Aside from that, we are solving a system of four equations for four unknowns. The first two equations are for mass A and the last two are for mass B.
F 1 ≈ 6 0 . 1 8 F 2 ≈ 7 9 . 8 6 F 3 ≈ 4 8 . 0 6 F 4 ≈ 2 6 3 . 7 8 F 2 + F 3 + F 4 ≈ 3 9 1 . 7 0