Calculating Force to Submerge 5 kg Object in Water

In summary, the force required to submerge a 5-kg object that displaces 10 kg of water is 49 N. This is because the buoyant force acting on the object is equal to the weight of the water displaced, which is 98.1 N. However, since the object also has a weight of 49 N, an equal or greater force must be applied to submerge it. This can be seen by drawing a free body diagram and considering all the forces acting on the object.
  • #1
physgrl
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Homework Statement



A 5-kg object displaces 10 kg of water. What is the force required to submerge the object?

a. 24 N

b. 147 N

c. 98 N

*d. 49 N

Homework Equations



Buoyant Force = Weight of the Water displaced

The Attempt at a Solution



Weight of the Water displaced=10kg*9.81m/s^2=98.1N

If the buoyant force is 98.1N an equal or greater force must be applied to submerge the object.

The answer key says its 49N...why?
 
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  • #2
You are forgetting about the weight of the object. If you draw a free body diagram and apply all the forces, it becomes obvious.
 
  • #3
Ohh right the object pushed downward too
 

1. How do you calculate the force needed to submerge a 5 kg object in water?

The formula for calculating the force needed to submerge an object in water is F = ρVg, where F is the force, ρ is the density of water (1000 kg/m3), V is the volume of the object, and g is the acceleration due to gravity (9.8 m/s2).

2. What is the density of water?

The density of water is 1000 kg/m3 at standard temperature and pressure.

3. How do you determine the volume of a 5 kg object?

The volume of an object can be determined by dividing its mass by its density. In this case, the volume of a 5 kg object can be found by dividing 5 kg by the density of water (1000 kg/m3), giving a volume of 0.005 m3.

4. How does the acceleration due to gravity affect the force needed to submerge an object?

The acceleration due to gravity affects the force needed to submerge an object because it determines the weight of the object. The greater the weight, the greater the force needed to submerge it in water.

5. Can this formula be used for objects with different densities?

Yes, this formula can be used for objects with different densities. However, the density of the object should be substituted for ρ in the formula. For example, if the object has a density of 800 kg/m3, the formula would become F = 800Vg.

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