Answer:
a) Mg/2
Explanation:
- if the rock is sitting on the bottom of the aquarium, this means that it is not accelerated in the vertical direction.
- In this direction , we have three forces acting on the rock:
- 1) Gravity, going downward.
- 2) Buoyant Force, going upward.
- 3) Normal Force, going upward.
- The gravity force, can be expressed in terms of the mass as the product of the density times volume, as follows:
[tex]F_{g} = \delta_{r} *V*g (1)[/tex]
- The buoyant force is equal to the weight of the water displaced by the rock, which can be expressed also in terms of the density, as follows:
[tex]F_{b} = \delta_{w} *V*g (2)[/tex]
- From the givens, we know that δr = 2*δw (3)
- Now, applying Newton's 2nd law in the vertical direction, as net force is zero, we have:
[tex]F_{g} =F_{b} + F_{n} (4)[/tex]
- Due to the normal force can take any value, we can write (4) as follows:
[tex]F_{n} = F_{g} -F_{b} (5)[/tex]
- Replacing Fg and Fb by (1) and(2), applying the condition (3), we get:
[tex]F_{n} =2* \delta_{w} *V*g - \delta_{w} *V*g = \delta_{w} *V*g (6)[/tex]
⇒ Fn = (m*g)/2
