A rectangular iron block of mass 10 kg is placed on the top of a table. The dimensions of the block are 20cm * 10cm * 5cm Find the pressure exerted by the block on the table if the block lies on the table with its sides of dimensions (i) 20cm * 10 cm and (ii) 10cm * 5cm What do you learn from this example? Take, g = 10m * s ^ - 2
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Answer:
To find the pressure exerted by the block on the table, we can use the formula for pressure:
Pressure (P) = Force (F) / Area (A)
First, let's calculate the force due to the weight of the block.
Given:
Mass of the block (m) = 10 kg
Acceleration due to gravity (g) = 10 m/s^2
The weight (force) of the block is given by:
F = m * g
F = 10 kg * 10 m/s^2
F = 100 N
Now, we need to find the area of contact between the block and the table for both cases.
(i) For the dimensions 20 cm x 10 cm:
Area (A) = Length (L) * Width (W)
A = 0.2 m * 0.1 m
A = 0.02 m^2
(ii) For the dimensions 10 cm x 5 cm:
Area (A) = Length (L) * Width (W)
A = 0.1 m * 0.05 m
A = 0.005 m^2
Now, we can calculate the pressure for both cases:
(i) Pressure for 20 cm x 10 cm:
P1 = F / A
P1 = 100 N / 0.02 m^2
P1 = 5000 Pa (Pascals)
(ii) Pressure for 10 cm x 5 cm:
P2 = F / A
P2 = 100 N / 0.005 m^2
P2 = 20000 Pa (Pascals)
What we learn from this example is that pressure depends on both force and the area over which the force is distributed. When the dimensions of the block in contact with the table are smaller (as in case ii), the pressure is higher for the same force. This is because the same force is distributed over a smaller area, resulting in higher pressure.
♦To find the pressure exerted by the block on the table, you can use the formula:
Pressure (P) = Force (F) / Area (A)
First, let's calculate the force due to the weight of the block, which is its mass (m) times the acceleration due to gravity (g):
F = m * g
F = 10 kg * 10 m/s^2
F = 100 N
Now, we need to find the area on which the block is resting for each case:
(i) When the block lies on the table with dimensions 20cm x 10cm, the area (A1) is:
A1 = 20 cm * 10 cm = 200 cm^2 = 0.02 m^2
(ii) When the block lies on the table with dimensions 10cm x 5cm, the area (A2) is:
A2 = 10 cm * 5 cm = 50 cm^2 = 0.005 m^2
Now we can find the pressure for both cases:
(i) Pressure (P1) = F / A1
P1 = 100 N / 0.02 m^2
P1 = 5000 N/m^2 or 5000 Pa (Pascal)
(ii) Pressure (P2) = F / A2
P2 = 100 N / 0.005 m^2
P2 = 20,000 N/m^2 or 20,000 Pa
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