Numerical problems

Problem 1

The average weight of an elephant is 4000 N. The surface area of the sole of its foot is 0.1m2. Calculate the pressure exerted by one foot of an elephant.

Solution

Average weight of the elephant = 4000 N

Weight of one leg = Force exerted by one leg

 = 4000/4 = 1000 N

 Area of the sole of one foot = 0.1 m2

Pressure = Force/Area

= 1000/0.1 = 10000 N/m2 = 104 Nm-2

Pressure exerted by one leg of the elephant is 10,000 newton on one square metre.

1. A stone weighs 500 N. Calculate the pressure exerted by it, if it makes contact with a surface of area 25 cm2.

Answer:

Given : Weight of a stone F = 500 N

Area A=25 cm2 = 25 × 10-4 m2

To find : Pressure P =?

Formula : Pressure P = F/A

= 500 / [25×10-4]

Solution:

Pressure P = 20 × 104 Nm-2 (or) 20 × 104 Pa

2. In a hydraulic lift, the surface area of the input piston is 10 cm2. The surface area of the output piston is 3000 cm2. A 100 N force applied to the input piston raises the output piston. Calculate the force required to raise the output piston.

Answer:

Solution :

Pressure input on piston,

P = F/A

= 100/ [10×10-4] = 105 N

According to Pascal’s law

P= F/A

105 =  F / [3000×10-4 ] = [ F×104 ] / 3000

104 × F = 105 × 3000

F = 3000 × 101

F = 3 × 104N