Pressure of solids – problems and solutions

1. Mass and volume of four blocks below are same. Which is the smaller pressure exerted by block on the floor?

Solution

P = F / A

Based on this formula it is concluded that pressure (P) is directly proportional to force (F) and inversely proportional to surface area (A).

The larger the force, the larger the pressure. The larger the surface area, the smaller the pressure.

Based on the picture, the largest surface area in contact with the floor is object III, so the pressure of object III on the floor is the smallest

2. If the mass of the four triangles below is the same, the greatest pressure on the floor is shown by the image …

Solution

P = F / A = w / A

*P = **pressure**, F = **force**, w = **weight**, A = **surface area*

Based on this formula it is concluded that pressure (P) is directly proportional to force (F) and inversely proportional to surface area (A).

The larger the force, the larger the pressure. The larger the surface area, the smaller the pressure.

The smallest surface area has the greatest pressure.

3. The greatest pressure is shown by image …

Solution

P = F / A = w / A

*P = **pressure**, F = **force**, w = **weight**, A = **surface area*

Based on this formula it is concluded that pressure (P) is directly proportional to force (F) and inversely proportional to surface area (A).

The larger the force, the larger the pressure. The larger the surface area, the smaller the pressure.

The smallest surface area has the greatest pressure.

4. The force of 500 Newton works on a surface of 2.5 m^{2}. Determine pressure.

__Known :__

Force (F) = 500 Newton

Surface area (A) = 2.5 m^{2}

__Wanted :__ Pressure (P)

__Solution :__

Pressure (P) :

P = F / A

P = 500 / 2.5

P = 200 N/m^{2}

P = 200 Pascal

5. Mass of a box = 75 kg and acceleration due to gravity (g) = 10 m/s^{2}. Determine the pressure on the floor.

__Known :__

Mass (m) = 75 kg

Acceleration due to gravity (g) = 10 m/s^{2}

Weight (w) = m g = (75 kg)(10 m/s^{2}) = 750 kg m/s^{2} = 750 Newton

Surface area (A) = 6 meters x 5 meters= 30 m^{2}

__Wanted :__ Pressure on the floor

__Solution :__

P = F/A = w/A = 750/30 = 25 N/m^{2}

6. Mass of a box is 24 kg. Acceleration due to gravity is 10 m/s^{2}. Determine the pressure on the floor.

__Known :__

Mass (m) = 24 kg

Acceleration due to gravity (g) = 10 m/s^{2}

Weight (w) = m g = (24 kg)(10 m/s^{2}) = 240 kg m/s^{2 }= 240 Newton

Surface area (A) = 1 m x 0.4 m = 0.4 m^{2}

__Wanted :__ The pressure on the floor

__Solution :__

P = F / A = w / A

*P = **pressure**, F = **force**, w = **weight**, A = **surface area*

Pressure on the floor :

P = 240 N / 0.4 m^{2} = 600 N/m^{2}

**What is pressure in the context of solids?****Answer**: Pressure is defined as the force exerted per unit area. When applied to solids, it refers to the force that a solid object applies to another surface divided by the contact area.

**How does the area of contact affect the pressure exerted by a solid object?****Answer**: The pressure exerted by a solid object is inversely proportional to the area of contact. If the force remains constant, increasing the contact area will decrease the pressure, and decreasing the contact area will increase the pressure.

**Why do sharp objects like needles and nails easily penetrate surfaces?****Answer**: Sharp objects have a very small contact area. When force is applied, this results in a high pressure at the tip, making it easier to penetrate other materials.

**How do snowshoes prevent a person from sinking deep into the snow?****Answer**: Snowshoes distribute the weight of a person over a larger surface area, reducing the pressure on the snow. This prevents or minimizes sinking.

**Why do heavy trucks have larger and wider tires than small cars?****Answer**: Larger and wider tires distribute the truck’s heavier weight over a greater surface area, reducing the pressure exerted on the road. This helps in preventing road damage and providing better traction.

**How does pressure relate to the depth in a column of solid?****Answer**: Unlike fluids, the pressure in solids does not continuously increase with depth in a predictable manner due to gravity alone. The pressure at a depth in a solid depends on both its weight above that point and the structural and material properties of the solid.

**Why might a heavy book not damage a table but a pointed object with much less weight can?****Answer**: The pressure exerted by an object is a function of both its weight and the area over which that weight is distributed. A heavy book distributes its weight over a large area, resulting in low pressure. A pointed object, even if lightweight, concentrates its force over a very small area, resulting in high pressure, which can damage the table.

**How does pressure distribution in solids affect building foundations?****Answer**: Building foundations distribute the weight of the structure over a large area, reducing the pressure on the ground beneath. Proper pressure distribution ensures that the building doesn’t sink or tilt due to uneven settling.

**Why do high heels often leave indentations on soft surfaces?****Answer**: High heels concentrate the wearer’s weight on a very small area, leading to high pressure at the point of contact. On soft surfaces, this high pressure can cause indentations or marks.

**If you press your hand against a wall, why doesn’t it sink into the wall like it might with a soft substance?**

**Answer**: The structural and material properties of the wall resist deformation, even when a force (your hand) is applied. While there’s pressure being exerted by your hand on the wall, the wall’s material is robust and rigid enough to resist the pressure, preventing your hand from sinking.