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Applications of Integration: Pressure and Force

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Wize University Calculus 1 Textbook > Applications of Integration for Physical Science

Pressure and Force

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A triangular trough contains a certain oil with weight density w=55 lbs/ft3w=55 \ \text{lbs}/\text{ft}^3. The cross section of the tank is shown below. How much force does the fluid exert on the tank when the tank is full?





More Pressure and Force Questions:
Practice: Pressure and Force
A triangular trough contains a certain oil with weight density δ=55 lbs/ft3\delta=55 \ \text{lbs}/\text{ft}^3. The cross section of the tank is shown below. How much force does the fluid exert on the side of the tank when the tank is full? Note that the sides of the tank are given by the equations y=5y=5, y=xy=x, and y=−xy=-x.
(a) 125δ125\delta (b) 25δ25\delta (c) 1253δ\frac{125}{3}\delta (d) 253δ\frac{25}{3}\delta (e) 250δ250\delta
Practice: Pressure and Force
A triangular trough contains a certain oil with weight density δ=55 lbs/ft3\delta=55 \ \text{lbs}/\text{ft}^3. The cross section of the tank is shown below. How much force does the fluid exert on the side of the tank when the tank is full? Note that the sides of the tank are given by the equations y=5y=5, y=xy=x, and y=−xy=-x.
Practice: Pressure and Force
A triangular trough contains a certain oil with weight density δ=55 lbs/ft3\delta=55 \ \text{lbs}/\text{ft}^3. The cross section of the tank is shown below. How much force does the fluid exert on the side of the tank when the tank is full? Note that the sides of the tank are given by the equations y=5y=5, y=xy=x, and y=−xy=-x.
Applications of Integration: Pressure and Force
A triangular trough contains a certain oil with weight density w=55 lbs/ft3w=55 \ \text{lbs}/\text{ft}^3. The cross section of the tank is shown below. How much force does the fluid exert on the tank when the tank is full?
New Practice Question
An engineer plans to design a levitating piston which can support loads up to 500kg. He decides to make a cylindrical chamber with radius of 0.5m with a moving piston which weighs 20kg. The chamber is filled with 10 moles of a diatomic ideal gas which is initially kept at 200K. By adding loads on the piston, the gas underneath is heated such that the height of the piston remains unchanged. (Assume that heating process is happening extremely fast such that the height of the piston remains constant while the gas is heated)
a) When there is no load on the piston, what is the pressure of the gas inside the chamber?
b) What is the temperature of the gas when maximum load is added to the piston?
Applications of Integration: Pressure and Force
The change in momentum, called impulse (J), is calculated mathematically as J=∫t0tfF(t)  ⁣dt\displaystyle J=\int_{t_0}^{t_f}F(t)\de{t} where F(t)F(t) is the force exerted on an object as a function of time over the interval from initial time t0t_0 to final time tft_f. Determine the impulse within 1 second using the force F(t)=∣t−0.9∣F(t)=|t-0.9|.