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

2. 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 0.028 m 2 =19 250 N/m 2 Pa = 19.25 N/m 2 kPa P P 55 kg 539 N

3. The sole of the boot she is walking on has an area of 0.028 square meters. P = F A = 539 N 0.028 m 2 =19 250 N/m 2 Pa = 19.25 N/m 2 kPa P P 55 kg 539 N The sole of a boot has a total area of 0.028 m 2.

4. So the pressure applied by the boot is equal to force divided by area P = F A = 539 N 0.028 m 2 =19 250 N/m 2 Pa = 19.25 N/m 2 kPa P P 55 kg 539 N The sole of a boot has a total area of 0.028 m 2. = F A = 539 N 0.028 m 2 = 19 250 2 Pa P P

5. Which is 539 N divided by 0.028 square meters P = F A = 539 N 0.028 m 2 =19 250 N/m 2 Pa = 19.25 N/m 2 kPa P P 55 kg 539 N The sole of a boot has a total area of 0.028 m 2. = F A = 539 N 0.028 m 2 = 19 250 2 Pa P P

6. Which comes out to 19 250 Pascals P = F A = 539 N 0.028 m 2 =19 250 N/m 2 Pa = 19.25 N/m 2 kPa P P 55 kg 539 N The sole of a boot has a total area of 0.028 m 2. = F A = 539 N 0.028 m 2 = 19 250 2 Pa P P

7. 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.

8. The pressure applied to the snow during this step is found to be 4492 Pascals, considerably less than the 19 250 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.

9. 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 = ?

10. 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 = ?

11. 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 = ?

12. 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

13. 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

14. 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

15. 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

16. 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

17. 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

18. 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

19. = 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 = ?

20. 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

21. 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 2 4492 N/m 2

22. 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 2 4492 N/m 2

23. 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 2 4492 N/m 2 N N/m 2 N m 2 / N = ×

24. = 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 2 4492 N/m 2 N N/m 2 N m 2 / N × Invert the divisor and multiply

25. = 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 2 4492 N/m 2 N N/m 2 N m 2 / N × Invert the divisor and multiply

26. = 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 2 4492 N/m 2 N N/m 2 m 2 / N × m2m2

27. = 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 2 4492 N/m 2 N N/m 2 × m2m2

28. = 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 2 4492 N/m 2 N N/m 2 × m2m2

29. = 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 2 4492 N/m 2 N N/m 2 × m2m2

30. 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 2 4492 N/m 2 A A = ? The area of the snowshoe is 0.12 m 2 539 N

31. BootSnowshoe Mass of person55 kg Force of Gravity539 N Area of Contact0.028 m 2 0.12 m 2 Pressure19 250 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.

32. BootSnowshoe Mass of person55 kg Force of Gravity539 N Area of Contact0.028 m 2 0.12 m 2 Pressure19 250 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.

33. BootSnowshoe Mass of person55 kg Force of Gravity539 N Area of Contact0.028 m 2 0.12 m 2 Pressure19 250 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.

34. BootSnowshoe Mass of person55 kg Force of Gravity539 N Area of Contact0.028 m 2 0.12 m 2 Pressure19 250 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.

35. BootSnowshoe Mass of person55 kg Force of Gravity539 N Area of Contact0.028 m 2 0.12 m 2 Pressure19 250 Pa4492 Pa The area of contact of the boot is 0.028 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.

36. BootSnowshoe Mass of person55 kg Force of Gravity539 N Area of Contact0.028 m 2 0.12 m 2 Pressure19 250 Pa4492 Pa And the pressure applied by the boot onto the snow is 19 250 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.

37. BootSnowshoe Mass of person55 kg Force of Gravity539 N Area of Contact0.028 m 2 0.12 m 2 Pressure19 250 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.

38. BootSnowshoe Mass of person55 kg Force of Gravity539 N Area of Contact0.028 m 2 0.12 m 2 Pressure19 250 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.

39. BootSnowshoe Mass of person55 kg Force of Gravity539 N Area of Contact0.028 m 2 0.12 m 2 Pressure19 250 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.

40. BootSnowshoe Mass of person55 kg Force of Gravity539 N Area of Contact0.028 m 2 0.12 m 2 Pressure19 250 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.

41. BootSnowshoe Mass of person55 kg Force of Gravity539 N Area of Contact0.028 m 2 0.12 m 2 Pressure19 250 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.

42. BootSnowshoe Mass of person55 kg Force of Gravity539 N Area of Contact0.028 m 2 0.12 m 2 Pressure19 250 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.

43. 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 2. 539 N  Smaller area of contact  Greater pressure  Will sink into the snow

44. 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 2. 539 N  Smaller area of contact  Greater pressure  Will sink into the snow

45. 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 2. 539 N  Smaller area of contact  Greater pressure  Will sink into the snow

46. 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 2. 539 N  Smaller area of contact  Greater pressure  Will sink into the snow  Greater area of contact  Lower pressure  Will not sink into the snow

47. 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 2. 539 N  Smaller area of contact  Greater pressure  Will sink into the snow  Greater area of contact  Lower pressure  Will not sink into the snow

48. 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 2. 539 N  Smaller area of contact  Greater pressure  Will sink into the snow  Greater area of contact  Lower pressure  Will not sink into the snow