Calculate Torque: Homework Solutions

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To solve the problem of forces exerted by two people holding a wooden board with a box on it, the total weight of the board and the box must be calculated, resulting in a combined force of 93.59 N. The forces exerted by each person cannot simply be the sum of the weights; instead, the torques must also be considered. By choosing a pivot point, typically where one person is holding the board, two equations can be established to find the individual forces. It is essential to account for both the vertical forces and the torques to arrive at the correct solution. Understanding these principles is crucial for accurately calculating the forces involved.
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Homework Statement



Two people are holding up the ends of a 4.55-kg wooden board that is l = 1.90 m long. A m = 5.00-kg box sits on the board, 0.50 m from one end, as shown below. What forces do the two people exert?


Homework Equations



T=F*d

The Attempt at a Solution


4.55*9.8=44.59N
5*9.8=49N
49N+44.59N=93.59N=Total Force

Length(left)=1.4m Length(right)=.5m


I am unsure how do you calculate the force each person exerts, or if I am missing an equation
 
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The total force is not just the sum of the weights. If the board is being held up, each person will exert a force on the board in the upwards direction. So you have four forces to sum up, not two. You also need to sum up the torques by picking one point to be your pivot point (it would be convenient to pick one of the points where a person is holding the board). This will give you two equations to work with.
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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