Here, we’ll show you how to calculate the area of a force being applied when we are given the force and the pressure.

In the previous problem, we discovered that a person with a 55 kg mass, has a force of gravity of 539 Newtons. P = F A = 539 N m 2 = N/m 2 Pa = N/m 2 kPa P P 55 kg 539 N

The sole of the boot she is walking on has an area of square meters. P = F A = 539 N m 2 = N/m 2 Pa = N/m 2 kPa P P 55 kg 539 N The sole of a boot has a total area of m 2.

So the pressure applied by the boot is equal to force divided by area P = F A = 539 N m 2 = N/m 2 Pa = N/m 2 kPa P P 55 kg 539 N The sole of a boot has a total area of m 2. = F A = 539 N m 2 = Pa P P

Which is 539 N divided by square meters P = F A = 539 N m 2 = N/m 2 Pa = N/m 2 kPa P P 55 kg 539 N The sole of a boot has a total area of m 2. = F A = 539 N m 2 = Pa P P

Which comes out to Pascals P = F A = 539 N m 2 = N/m 2 Pa = N/m 2 kPa P P 55 kg 539 N The sole of a boot has a total area of m 2. = F A = 539 N m 2 = Pa P P

In this problem, we’ll consider the same 55 kg person, with a gravitational force of 539 N taking a step with one foot on a snowshoe this time instead of a boot. 55 kg 539 N A 55 kg person with a gravitational force of 539 N takes a step with one foot that is wearing a snowshoe.

The pressure applied to the snow during this step is found to be 4492 Pascals, considerably less than the Pascals applied by the boot. 55 kg 539 N P = 4492 Pa = 4492 N/m 2 A 55 kg person with a gravitational force of 539 N takes a step with one foot that is wearing a snowshoe. The pressure applied to the snow in this case is 4492 Pa.

A snowshoe applies less pressure for the same force of gravity because the force is distributed over a larger area than the sole a boot. We’re asked for the area of contact the snowshoe has with the snow. 55 kg 539 N P = 4492 Pa = 4492 N/m 2 A 55 kg person with a gravitational force of 539 N takes a step with one foot that is wearing a snowshoe. The pressure applied to the snow in this case is 4492 Pa. What is the area of the snowshoe in m 2 ? A = ?

Remember that pressure, expressed as 4492 Pascals, 539 N P = 4492 Pa = 4492 N/m 2 A person with a gravitational force of 539 N takes a step with a snowshoe. The pressure applied is 4492 Pa. What is the area of the snowshoe in m 2 ? A = ?

is the same as 4492 Newtons per square meter. 539 N P = 4492 Pa = 4492 N/m 2 A person with a gravitational force of 539 N takes a step with a snowshoe. The pressure applied is 4492 Pa. What is the area of the snowshoe in m 2 ? A = ?

The formula for pressure is pressure equals force divided by area, or P equals F divided by A. 539 N P = 4492 Pa = 4492 N/m 2 A person with a gravitational force of 539 N takes a step with a snowshoe. The pressure applied is 4492 Pa. What is the area of the snowshoe in m 2 ? A = ? P = F A

Were asked to find the area of the snowshoe so we rearrange this equation to solve for area, A 539 N P = 4492 Pa = 4492 N/m 2 A person with a gravitational force of 539 N takes a step with a snowshoe. The pressure applied is 4492 Pa. What is the area of the snowshoe in m 2 ? A = ? P = F A Solve for Area

We start by multiplying both sides of the equation by A (click) 539 N P = 4492 Pa = 4492 N/m 2 A person with a gravitational force of 539 N takes a step with a snowshoe. The pressure applied is 4492 Pa. What is the area of the snowshoe in m 2 ? A = ? P = F A A A ×× P = F A × = F P A

A is in the numerator and denominator on the right side, so it can be cancelled out, (click) leaving us with only F on the right side. 539 N P = 4492 Pa = 4492 N/m 2 A person with a gravitational force of 539 N takes a step with a snowshoe. The pressure applied is 4492 Pa. What is the area of the snowshoe in m 2 ? A = ? P = F A A A ×× P = F A × = F P A

So we’re left with the equation A times P equals F 539 N P = 4492 Pa = 4492 N/m 2 A person with a gravitational force of 539 N takes a step with a snowshoe. The pressure applied is 4492 Pa. What is the area of the snowshoe in m 2 ? A = ? P = F A × = F P A Solve for Area

In order to solve this equation for A, we divide both sides of the equation by P (click) 539 N P = 4492 Pa = 4492 N/m 2 A person with a gravitational force of 539 N takes a step with a snowshoe. The pressure applied is 4492 Pa. What is the area of the snowshoe in m 2 ? A = ? P = F A × P Solve for Area F PP

A P is on in the numerator and denominator on the left side, so it can be cancelled, (click), leaving us with only A on the left side. 539 N P = 4492 Pa = 4492 N/m 2 A person with a gravitational force of 539 N takes a step with a snowshoe. The pressure applied is 4492 Pa. What is the area of the snowshoe in m 2 ? A = ? P = F × F PP

= F A F P We’ll just move the equation over here. (click) 539 N P = 4492 Pa = 4492 N/m 2 A person with a gravitational force of 539 N takes a step with a snowshoe. The pressure applied is 4492 Pa. What is the area of the snowshoe in m 2 ? A = ?

In order to solve for A We’ll start by substituting 539 Newtons in for force. 539 N P = 4492 Pa = 4492 N/m 2 A person with a gravitational force of 539 N takes a step with a snowshoe. The pressure applied is 4492 Pa. What is the area of the snowshoe in m 2 ? A = ? = F A F P = 539 N 4492 N/m 2 = 0.12 m 2

Then we’ll substitute 4492 Newtons per square meter in for pressure 539 N P = 4492 Pa = 4492 N/m 2 A person with a gravitational force of 539 N takes a step with a snowshoe. The pressure applied is 4492 Pa. What is the area of the snowshoe in m 2 ? A = ? = F A F P = 539 N = 0.12 m N/m 2

539 divided by 4492 is equal to 0.12 A person with a gravitational force of 539 N takes a step with a snowshoe. The pressure applied is 4492 Pa. What is the area of the snowshoe in m 2 ? = F A F P = 539 N = 0.12 m N/m 2

Looking at the units, Newtons are divided by the fraction Newtons per square meter A person with a gravitational force of 539 N takes a step with a snowshoe. The pressure applied is 4492 Pa. What is the area of the snowshoe in m 2 ? = F A F P = 539 N = 0.12 m N/m 2 N N/m 2 N m 2 / N = ×

= In order to divide by a fraction we invert the divisor and multiply, A person with a gravitational force of 539 N takes a step with a snowshoe. The pressure applied is 4492 Pa. What is the area of the snowshoe in m 2 ? = F A F P = 539 N = 0.12 m N/m 2 N N/m 2 N m 2 / N × Invert the divisor and multiply

= giving us Newtons times square meters over Newtons A person with a gravitational force of 539 N takes a step with a snowshoe. The pressure applied is 4492 Pa. What is the area of the snowshoe in m 2 ? = F A F P = 539 N = 0.12 m N/m 2 N N/m 2 N m 2 / N × Invert the divisor and multiply

= N Newtons will cancel out (click) A person with a gravitational force of 539 N takes a step with a snowshoe. The pressure applied is 4492 Pa. What is the area of the snowshoe in m 2 ? = F A F P = 539 N = 0.12 m N/m 2 N N/m 2 m 2 / N × m2m2

= N Leaving us with square meters as a unit A person with a gravitational force of 539 N takes a step with a snowshoe. The pressure applied is 4492 Pa. What is the area of the snowshoe in m 2 ? = F A F P = 539 N = 0.12 m N/m 2 N N/m 2 × m2m2

= N Which we’ll write down here A person with a gravitational force of 539 N takes a step with a snowshoe. The pressure applied is 4492 Pa. What is the area of the snowshoe in m 2 ? = F A F P = 539 N = 0.12 m N/m 2 N N/m 2 × m2m2

= N So the final answer is A person with a gravitational force of 539 N takes a step with a snowshoe. The pressure applied is 4492 Pa. What is the area of the snowshoe in m 2 ? = F A F P = 539 N = 0.12 m N/m 2 N N/m 2 × m2m2

the area of the snowshoe is 0.12 square meters A person with a gravitational force of 539 N takes a step with a snowshoe. The pressure applied is 4492 Pa. What is the area of the snowshoe in m 2 ? = F A F P = 539 N = 0.12 m N/m 2 A A = ? The area of the snowshoe is 0.12 m N

BootSnowshoe Mass of person55 kg Force of Gravity539 N Area of Contact0.028 m m 2 Pressure Pa4492 Pa In this table, we’ll compare the mass and force of gravity of the person, the area of contact, and the pressure applied by taking a step with a boot and with a snowshoe A person with a gravitational force of 539 N takes a step with a snowshoe. The pressure applied is 4492 Pa. The area of the snowshoe is 0.12 m 2.

BootSnowshoe Mass of person55 kg Force of Gravity539 N Area of Contact0.028 m m 2 Pressure Pa4492 Pa We’ll start with the boot A person with a gravitational force of 539 N takes a step with a snowshoe. The pressure applied is 4492 Pa. The area of the snowshoe is 0.12 m 2.

BootSnowshoe Mass of person55 kg Force of Gravity539 N Area of Contact0.028 m m 2 Pressure Pa4492 Pa The person wearing the boot has a mass of 55 kg A person with a gravitational force of 539 N takes a step with a snowshoe. The pressure applied is 4492 Pa. The area of the snowshoe is 0.12 m 2.

BootSnowshoe Mass of person55 kg Force of Gravity539 N Area of Contact0.028 m m 2 Pressure Pa4492 Pa Which means she has a force of gravity of 539 Newtons acting on her. A person with a gravitational force of 539 N takes a step with a snowshoe. The pressure applied is 4492 Pa. The area of the snowshoe is 0.12 m 2.

BootSnowshoe Mass of person55 kg Force of Gravity539 N Area of Contact0.028 m m 2 Pressure Pa4492 Pa The area of contact of the boot is square meters. A person with a gravitational force of 539 N takes a step with a snowshoe. The pressure applied is 4492 Pa. The area of the snowshoe is 0.12 m 2.

BootSnowshoe Mass of person55 kg Force of Gravity539 N Area of Contact0.028 m m 2 Pressure Pa4492 Pa And the pressure applied by the boot onto the snow is Pascals. Because this pressure is so high, the boot will likely sink into the snow. A person with a gravitational force of 539 N takes a step with a snowshoe. The pressure applied is 4492 Pa. The area of the snowshoe is 0.12 m 2.

BootSnowshoe Mass of person55 kg Force of Gravity539 N Area of Contact0.028 m m 2 Pressure Pa4492 Pa Now, we’ll consider these quantities when she takes a step with a snowshoe. A person with a gravitational force of 539 N takes a step with a snowshoe. The pressure applied is 4492 Pa. The area of the snowshoe is 0.12 m 2.

BootSnowshoe Mass of person55 kg Force of Gravity539 N Area of Contact0.028 m m 2 Pressure Pa4492 Pa Her mass is still 55 kg. Here, we’ll ignore any difference in mass that would result by putting on the snowshoe. A person with a gravitational force of 539 N takes a step with a snowshoe. The pressure applied is 4492 Pa. The area of the snowshoe is 0.12 m 2.

BootSnowshoe Mass of person55 kg Force of Gravity539 N Area of Contact0.028 m m 2 Pressure Pa4492 Pa The force of gravity acting on her is still 539 Newtons. A person with a gravitational force of 539 N takes a step with a snowshoe. The pressure applied is 4492 Pa. The area of the snowshoe is 0.12 m 2.

BootSnowshoe Mass of person55 kg Force of Gravity539 N Area of Contact0.028 m m 2 Pressure Pa4492 Pa The area of contact of the snowshoe is 0.12 square meters. The snowshoe distributes the force over an area greater than 4 times than the boot. A person with a gravitational force of 539 N takes a step with a snowshoe. The pressure applied is 4492 Pa. The area of the snowshoe is 0.12 m 2.

BootSnowshoe Mass of person55 kg Force of Gravity539 N Area of Contact0.028 m m 2 Pressure Pa4492 Pa Finally, the pressure the snowshoe applies to the snow is only 4492 Pascals. This is less that a quarter of the pressure applied by the boot. A person with a gravitational force of 539 N takes a step with a snowshoe. The pressure applied is 4492 Pa. The area of the snowshoe is 0.12 m 2.

BootSnowshoe Mass of person55 kg Force of Gravity539 N Area of Contact0.028 m m 2 Pressure Pa4492 Pa This low pressure applied to the snow means the snowshoe will not sink into the snow as much as the boot did. A person with a gravitational force of 539 N takes a step with a snowshoe. The pressure applied is 4492 Pa. The area of the snowshoe is 0.12 m 2.

To summarize, we saw that the boot has a smaller area of contact A person with a gravitational force of 539 N takes a step with a snowshoe. The pressure applied is 4492 Pa. The area of the snowshoe is 0.12 m N  Smaller area of contact  Greater pressure  Will sink into the snow

Which results in a greater pressure A person with a gravitational force of 539 N takes a step with a snowshoe. The pressure applied is 4492 Pa. The area of the snowshoe is 0.12 m N  Smaller area of contact  Greater pressure  Will sink into the snow

So the boot will likely sink into the snow A person with a gravitational force of 539 N takes a step with a snowshoe. The pressure applied is 4492 Pa. The area of the snowshoe is 0.12 m N  Smaller area of contact  Greater pressure  Will sink into the snow

The snowshoe has a greater area of contact A person with a gravitational force of 539 N takes a step with a snowshoe. The pressure applied is 4492 Pa. The area of the snowshoe is 0.12 m N  Smaller area of contact  Greater pressure  Will sink into the snow  Greater area of contact  Lower pressure  Will not sink into the snow

Which results in a lower pressure A person with a gravitational force of 539 N takes a step with a snowshoe. The pressure applied is 4492 Pa. The area of the snowshoe is 0.12 m N  Smaller area of contact  Greater pressure  Will sink into the snow  Greater area of contact  Lower pressure  Will not sink into the snow

Therefore, the snowshoe will not sink into the snow as much as the boot did. This is how snowshoes work. A person with a gravitational force of 539 N takes a step with a snowshoe. The pressure applied is 4492 Pa. The area of the snowshoe is 0.12 m N  Smaller area of contact  Greater pressure  Will sink into the snow  Greater area of contact  Lower pressure  Will not sink into the snow