When a crown of mass 14.7 kg is submerged in water, an accurate scale reads only 13.4 kg. Is the crown made of real gold?
Ok How do I do this problem
I set up my free body diagram
Net Force = ma = 0= Ft + Fb - Fg
were Ft is the force of tension on the scale that was used to measure it's apparent weight
- Ft = Fb - Fg
Ft = Fg - Fb
Ft = (mass of object)g - (density of fluid)g(volume of fluid)
density of object = (mass of object)/(volume of object)
mass of object = (density of object)(volume of object)
plug chug
Ft = (density of object) (volume of object)g - (density of fluid)g(volume of fluid)
ok were do I go from here I think that the volumes are suppose to be the same but I do not see how.
IF the thing is submerged, then
volume=mass/densitymaterial
The bouyant force is volumedisplaced*denstitywater.
bouyantforce= 14.7/densitymaterial*density water.
according to the measurements, the bouyant force is 14.7-13.3=1.4g
then calculate the density of material:
density material= 14.7/1.4 * 1g/cm^3
which is about 10.5g/cm^3 So is this Gold?
why are the volumes the same
Fg on object = (it's density)(it's volume)g
Fb = (density of water)(volume of water underneath object pushing it up)gravity
your suppose to divide the two gravity is suppose to cancel out and the volume but the volumes are two different objects why are they the same
What objects do you know when submerged change volume? Certainly chunks of metal do not.
9.8
To determine if the crown is made of real gold, we can use the principle of buoyancy. When an object is submerged in a fluid, it experiences an upward buoyant force equal to the weight of the fluid displaced by the object.
Let's consider the forces acting on the crown when it is submerged in water:
- The force of tension on the scale (Ft)
- The buoyant force due to the water (Fb)
- The force of gravity acting on the crown (Fg)
Based on the given information, the scale reads a weight of 13.4 kg, which is less than the actual weight of the crown (14.7 kg). This indicates that the buoyant force (Fb) is greater than the actual weight of the crown.
We can calculate the buoyant force using the formula: Fb = (density of fluid) * g * (volume of fluid)
The volume of fluid displaced by the crown is equal to the volume of the crown itself. So, we need to find the volume of the crown.
To find the volume of the crown, we can use the density of an object formula: density = (mass of object) / (volume of object)
Rearranging this formula, we get: volume of object = (mass of object) / (density of object)
Since we know the mass of the crown (14.7 kg) and the density of gold (19,300 kg/m^3), we can calculate the volume of the crown.
Now, substitute the values into the formula for the buoyant force.
Fb = (density of fluid) * g * (volume of crown)
The density of water is approximately 1000 kg/m^3, and g is the acceleration due to gravity, which is 9.8 m/s^2.
With these values, you can solve for Fb.
Next, we can find the force of tension on the scale (Ft). Since the scale measures the apparent weight of the crown, Ft is equal to the difference between the actual weight of the crown (Fg) and the buoyant force (Fb).
Ft = Fg - Fb
If Ft is positive, it means the scale is measuring a greater weight than the actual weight of the crown. If Ft is negative, it means the scale is measuring a lower weight than the actual weight of the crown.
If Ft is negative, then the crown is less dense than water (density of object < density of water), which means it is not made of real gold.