Two people are moving a table into their new home

Question

Two people are moving a 25kg table into their new home. The table is 2.2m long. One stands at one end, the other person stands 30cm from the other end. Calculate the lifting force required of the person not standing at the end. g=9.8Nkg^-1

Answer 1

For this problem, I have to first assume that the 2 people are keeping the table level (not in the process of lifting/lowering it and it's not rotating). Otherwise, we don't have enough info to solve this. The basic plan here is to use our equilibrium equations to get a system of 2 equations that we can solve.

1. Remember that the equilibrium equations are that the horizontal forces, the vertical forces, and the moments must all add up to 0.
2. Horizontal forces: There are none - ignore this.
3. Vertical forces: There are 3
4. The weight of the table is W = 25g
5. The vertical forces of the 2 movers must add up to 25g to counter that weight.
6. You can write F₁ + F₂ = 25g
7. It doesn't matter, but let's say F₁ is the mover at the end and F₂ is the one we want to solve for.
8. Moments: There are 2, caused by the 2 upward forces of the movers. If the movers were on opposite ends of the table, the forces would have to be equal -- this would be an easy problem.
9. Write an expression for the moment that each force creates.
10. The table will be rotating about its center.
11. M₁ = F₁ * 1.1 m clockwise (depending on your drawing)
12. Note that the distance is half of the length of the table.
13. M₂ = F₂ (1.1m - 0.30m) = F₂ *0.80 m CCW (opposite the other moment
14. We subtract the 30 cm from half the length of the table to find the distance.
15. These moments must be equal and opposite, so we can write:
16. 1.1 * F₁ = 0.8 *F₂
17. From this, we can see that the mover that's closer to the center will have to provide a larger share of the upward force, which makes some sense, since they're close to the center.
18. Combine the equations
19. Since we're solving for F₂, we want to try to get rid of F₁ from our equations. A good way is to use the 2 equations you have to write an expression for F₁ in terms of F₂, then go move that expression into the other equation.
20. From part 1, F₁ + F₂ = 25g, which we can write as F₁ = 25g - F₂
21. From part 2, 1.1 * F₁ = 0.8 *F₂
22. Plugging in, 1.1 * (25g - F₂) = 0.8 * F₂
23. Solve this for F₂ and you've got your answer.
24. Check: Does your answer make sense? The value should be less than the weight of the table, and larger than half the weight of the table.