A 73 kg man in a 7.0 kg chair tilts back so that all the weight is balanced on two legs of the chair. Assume that each leg makes contact with the floor over a circular area with a radius of 1.0 cm, and find the pressure exerted on the floor by each leg.
pressureEachLeg= weight/area * 1/2
so would it be...
P=((73+7)*9.8)/2*pi*r then divide it by 2?
or would it be...
4P=((73+7)*9.8)/2*pi*r then divide it by 2?
No. Area of a circle is PI r^2
so the denominator is / PI r^2 *1/2
which changes all to
pressure= 2*80*g/PI(.01)^2
To find the pressure exerted on the floor by each leg, we need to calculate the force exerted by each leg and then divide it by the area of contact.
First, we find the force exerted by each leg. Since the weight of the man and the chair is balanced on two legs, the force exerted by each leg would be half the total weight.
The weight of the man and the chair is given as 73 kg + 7.0 kg = 80 kg.
So, the force exerted by each leg can be calculated as: Force = Weight/2 = 80 kg / 2 = 40 kg.
Now, we need to calculate the area of contact for each leg. The area of a circle can be calculated using the formula: Area = π * r^2, where r is the radius.
Given radius = 1.0 cm = 0.01 m.
The area of contact for each leg is: Area = π * (0.01 m)^2 = 0.0001 π m^2.
Finally, we can calculate the pressure exerted on the floor by each leg using the formula: Pressure = Force / Area.
Plugging in the values, we get: Pressure = 40 kg / (0.0001 π m^2).
So, the pressure exerted on the floor by each leg is 400,000 π kg/m^2, or approximately 1,256,637.06 kg/m^2 (rounded to two decimal places).
Therefore, the pressure exerted on the floor by each leg is approximately 1,256,637.06 kg/m^2.