a 5 cm^3 block of lead weighs 0.55 N. The lead is carefully submerged in a tank of mercury. One cm^3 of mercury weighs 0.13 N. What is the weight of the mercury displaced by the block of lead? Will the block of lead sink or float in the mercury?
Explain with steps
Answers
Answer:
Explanation:Archimedes Principle Worksheet Answers
More than 2,000 years ago, Archimedes discovered the relationship between buoyant force and how much fluid
is displaced by an object. Archimedes principle states:
The buoyant force acting on an object in a fluid is equal to the weight of the fluid displaced by the object.
We can practice figuring out the buoyant force using a beach ball and a big tub of water. Our beach ball has a
volume of 14,130 cm3
. The weight of the beach ball in air is 1.5 N.
If you put the beach ball into the water and don’t push down on it, you’ll see that
the beach ball floats on top of the water by itself. Only a small part of the beach
ball is underwater. Measuring the volume of the beach ball that is under water, we
find it is 153 cm3
. Knowing that 1 cm3
of water has a mass of 1 g, you can
calculate the weight of the water displaced by the beach ball.
153 cm3
of water = 153 grams = 0.153 kg
weight = mass force of gravity per kg = (0.153 kg) 9.8 N/kg =
1.5 N
According to Archimedes principle, the buoyant force acting on the
beach ball equals the weight of the water displaced by the beach
ball. Since the beach ball is floating in equilibrium, the weight of
the ball pushing down must equal the buoyant force pushing up on
the ball. We just showed this to be true for our beach ball.
Have you ever tried to hold a beach ball underwater? It takes a lot
of effort! That is because as you submerge more of the beach ball, the more the buoyant force acting on the ball
pushes it up. Let’s calculate the buoyant force on our beach ball if we push it all the way under the water.
Completely submerged, the beach ball displaces 14,130 cm3
of water. Archimedes principle tells us that the
buoyant force on the ball is equal to the weight of that water:
14,130 cm3
of water = 14,130 grams = 14.13 kg
weight = mass force of gravity per kg = (14.13 kg) 9.8 N/kg = 138 N
If the buoyant force is pushing up with 138 N, and the weight of the ball is only 1.5 N, your pushing down on
the ball supplies the rest of the force, 136.5 N.
A 10-cm3
block of lead weighs 1.1 N. The lead is placed in a tank of water. One cm3
of water weighs 0.0098 N.
What is the buoyant force on the block of lead?
Given:
Weight of lead block = 1.1 N
Volume of block = 10 cm3
Solution:
The lead displaces 10 cm3
of water.
buoyant force = weight of water displaced
10 cm3 of water 0.0098 N/cm3
Looking for: = 0.098 N
Buoyant force on the lead block
Relationships:
1 cm
3
of water weighs 0.0098 N.
1. A block of gold and a block of wood both have the same volume. If they are both submerged in water,
which has the higher buoyant force? Answer – if they are both submerged, they displace the same amount of
fluid, therefore their buoyant force is the same.
2. A 100-cm3
block of lead that weighs 11 N is carefully submerged in water. One cm3
of water weighs 0.0098
N.
a. What volume of water does the lead displace? Answer – 100 cm3
b. How much does that volume of water weigh? Answer – 0.0098 x 100 = 0.98 N
c. What is the buoyant force on the lead? Answer - 0.98 N
d. Will the lead block sink or float in the water? Answer -sink
3. The same 100-cm3
lead block is carefully submerged in a container of mercury. One cm3
of mercury weighs
0.13 N.
a. What volume of mercury is displaced? Answer – 100 cm3
b. How much does that volume of mercury weigh? Answer – 0.13 x 100 = 13 N
c. What is the buoyant force on the lead? Answer -13 N
d. Will the lead block sink or float in the mercury? Answer - float
4. According to problems 2 and 3, does an object’s density have anything to do with whether or not it will float
in a particular liquid? Justify your answer. Answer – if an object is denser than the fluid it is placed in it will
sink, if the object is less dense than the fluid it will float.
5. Based on the table of densities, explain whether the object would float or sink in the following situations:
material density (g/ cm3
)
gasoline 0.7
gold 19.3
lead 11.3
mercury 13.6
molasses 1.37
Paraffin(wax) 0.87
platinum 21.4
a. A block of solid paraffin (wax) in molasses. Answer - floats
b. A bar of gold in mercury. Answer - sink
c. A piece of platinum in gasoline. Answer - sinks
d. A block of paraffin in gasoline. Answer -sink