To place a note on a cork board, you use a thumbtack with a force of 12 N. The radii of the head and tip of the tack is 5.5 mm and 0.2 mm, respectively. Find the:
(a) pressure applied to the head of the tack; and
(b) pressure exerted by the tip of the tack on the board.
pressure is force/area
so figure the areas and then divide. You will get N/mm^2
thx
To find the pressure applied to the head of the tack and the pressure exerted by the tip of the tack on the board, we can use the formula for pressure:
Pressure = Force / Area
(a) To find the pressure applied to the head of the tack, we need to find the area of the head.
Given:
Force = 12 N
Radius of the head (r) = 5.5 mm
First, we need to convert the radius to meters:
r = 5.5 mm = 5.5 / 1000 m = 0.0055 m
The area of the head is given by the formula:
Area = π * r^2
Plugging in the values:
Area = π * (0.0055 m)^2
Now, we can calculate the pressure:
Pressure (head) = Force / Area
(b) To find the pressure exerted by the tip of the tack on the board, we need to find the area of the tip.
Given:
Force = 12 N
Radius of the tip (r) = 0.2 mm
First, we need to convert the radius to meters:
r = 0.2 mm = 0.2 / 1000 m = 0.0002 m
The area of the tip (which is a circle) is given by the formula:
Area = π * r^2
Plugging in the values:
Area = π * (0.0002 m)^2
Now, we can calculate the pressure:
Pressure (tip) = Force / Area
Simplifying the equations will give us the final answers.
To solve this problem, we need to calculate the pressure applied to both the head of the tack and the tip of the tack. Pressure is defined as the force applied per unit area:
Pressure = Force / Area
(a) Pressure applied to the head of the tack:
The area of the head of the tack can be approximated as a circle:
Area = π * (radius of the head)^2
Given that the radius of the head of the tack is 5.5 mm (or 0.0055 m), we can calculate the area:
Area = π * (0.0055 m)^2
Now, we can use the equation for pressure to find the pressure applied to the head of the tack:
Pressure = 12 N / Area
Substituting the area value we calculated earlier, we get:
Pressure = 12 N / (π * (0.0055 m)^2)
(b) Pressure exerted by the tip of the tack on the board:
The area of the tip of the tack can also be approximated as a circle:
Area = π * (radius of the tip)^2
Given that the radius of the tip of the tack is 0.2 mm (or 0.0002 m), we can calculate the area:
Area = π * (0.0002 m)^2
Now, we can use the equation for pressure to find the pressure exerted by the tip of the tack on the cork board:
Pressure = 12 N / Area
Substituting the area value we calculated earlier, we get:
Pressure = 12 N / (π * (0.0002 m)^2)
To solve for the pressures, you can now use a calculator to compute the numerical values.