A car misses a turn and sinks into a shallow lake to a depth of 8.9 m. If the area of the car door is 0.51 m2, what is the force exerted on the outside of the door by the water? Note: 1 atm = 101.325 kPa.
What is the force exerted on the inside of the door by the air, assuming the inside of the car is at atmospheric pressure? Think about what the occupant should do to get the door open.
To determine the force exerted on the outside of the car door by the water, we can use the concept of pressure and the formula:
Pressure = Force / Area
First, we need to calculate the pressure exerted by the water on the door. The pressure at a certain depth in a fluid is given by the equation:
Pressure = density x gravitational acceleration x depth
In this case, the density of water is approximately 1000 kg/m³, and the gravitational acceleration is approximately 9.8 m/s². The depth is given as 8.9 m. Therefore, the pressure exerted by the water on the door can be calculated as:
Pressure = 1000 kg/m³ x 9.8 m/s² x 8.9 m
Next, we need to convert the pressure in Pascals to kilopascals using the conversion factor provided:
Pressure (kPa) = Pressure (Pa) / 1000
To find the force exerted on the outside of the door, we can rearrange the formula for pressure:
Force = Pressure x Area
Finally, we can substitute the values we have into the equation to find the force exerted on the outside of the door by the water.
To find the force exerted on the inside of the door by the air, assuming the inside of the car is at atmospheric pressure, we can use the same formula for pressure. However, in this case, the pressure will be atmospheric pressure, which is 101.325 kPa. We can substitute the values into the formula to find the force exerted on the inside of the door by the air.
To open the door, the occupant should decrease the pressure inside the car. This can be done by rolling down a window or opening another door slightly, allowing air to enter or escape and equalize the pressure inside and outside the car. Once the pressures are equalized, the door should be easier to open.