Q8: A boy presses a thumbtack into a piece of wood with a force of 20 N.
The surface area of the head of the thumbtack is 1 cm² and the cross-sectional
area of the tip is 0.01 cm².
a) Find the pressure on the head of the thumbtack.
b) Find the pressure exerted by the tip on the wood.
c) What conclusion can be drawn?
a) Find the pressure on the head of the thumbtack.
b) Find the pressure exerted by the tip on the wood.
c) What conclusion can be drawn?
Given:
Force, F = 20 N
Area of head = 1 cm² = 1 × 10⁻⁴ m²
Area of tip = 0.01 cm² = 1 × 10⁻⁶ m²
Formula: Pressure = Force / Area
a) Pressure on head:
P₁ = 20 / (1 × 10⁻⁴) = 2 × 10⁵ Pa
b) Pressure on tip:
P₂ = 20 / (1 × 10⁻⁶) = 2 × 10⁷ Pa
c) Conclusion:
Pressure is inversely proportional to area. Smaller area produces greater pressure, which allows the thumbtack to penetrate the wood.
Answer:
a) 2 × 10⁵ Pa
b) 2 × 10⁷ Pa
c) Smaller area → greater pressure
Force, F = 20 N
Area of head = 1 cm² = 1 × 10⁻⁴ m²
Area of tip = 0.01 cm² = 1 × 10⁻⁶ m²
Formula: Pressure = Force / Area
a) Pressure on head:
P₁ = 20 / (1 × 10⁻⁴) = 2 × 10⁵ Pa
b) Pressure on tip:
P₂ = 20 / (1 × 10⁻⁶) = 2 × 10⁷ Pa
c) Conclusion:
Pressure is inversely proportional to area. Smaller area produces greater pressure, which allows the thumbtack to penetrate the wood.
Answer:
a) 2 × 10⁵ Pa
b) 2 × 10⁷ Pa
c) Smaller area → greater pressure
Q9: The figure shows a hydraulic system with small and large pistons of areas
0.005 m² and 0.1 m² respectively. A force of 20 N is applied to the small piston.
Calculate:
a) Pressure transmitted in the fluid
b) Force on the large piston
c) Discuss the distance travelled by both pistons
a) Pressure transmitted in the fluid
b) Force on the large piston
c) Discuss the distance travelled by both pistons
Given:
Force on small piston, F₁ = 20 N
Area of small piston, A₁ = 0.005 m²
Area of large piston, A₂ = 0.1 m²
Principle: Pascal’s Law
a) Pressure in hydraulic fluid:
P = F₁ / A₁ = 20 / 0.005 = 4000 Pa
b) Force on large piston:
F₂ = P × A₂ = 4000 × 0.1 = 400 N
c) Distance travelled:
The small piston moves a greater distance while the large piston moves a smaller distance. This is because force is multiplied at the cost of distance.
Answer:
a) 4000 Pa
b) 400 N
c) Small piston moves more, large piston moves less
Force on small piston, F₁ = 20 N
Area of small piston, A₁ = 0.005 m²
Area of large piston, A₂ = 0.1 m²
Principle: Pascal’s Law
a) Pressure in hydraulic fluid:
P = F₁ / A₁ = 20 / 0.005 = 4000 Pa
b) Force on large piston:
F₂ = P × A₂ = 4000 × 0.1 = 400 N
c) Distance travelled:
The small piston moves a greater distance while the large piston moves a smaller distance. This is because force is multiplied at the cost of distance.
Answer:
a) 4000 Pa
b) 400 N
c) Small piston moves more, large piston moves less
