Hydostatics: Force and torque on a dam wall of reservoir

As the reservoir behind a dam is filled with water, the pressure that the water exerts on the dam increases. Eventually, the force on the dam becomes substantial, and it could cause the dam to collapse. There are two significant issues to be considered: First, the base of the dam should be able to withstand the pressure rho gh, where rho is the density of the water behind the dam, h is its depth, and g is the magnitude of the acceleration due to gravity. This means that the material of which the dam is made needs to be strong enough so that it doesn't crack (compressive strength).

The second issue has to do with the strength of the foundation of the dam. The water pressure exerts a clockwise torque on the dam, as shown in the figure. The foundation of the dam should be strong enough so that the dam does not topple. The material has to be strong enough that the dam does not snap (shear strength).

To study this phenomenon, consider the simple model of a dam depicted in the diagram. View Figure A reservoir of water (density rho) behind the dam is filled to a height h. Assume that the width of the dam (the dimension pointing into the screen) is L

a). Consider a horizontal layer of the dam wall of thickness dx located a distance x above the reservoir floor. What is the magnitude dF of the force on this layer due to the water in the reservoir? (in terms of x, dx, or other terms in the problem)

b) The force of the water produces a torque on the dam. In a simple model, if the torque due to the water were enough to cause the dam to break free from its foundation, the dam would pivot about its base (point P). What is the magnitude tau of the torque about the point P due to the water in the reservoir?
Express your answer in terms of quantities given in the problem introduction and the magnitude of the acceleration due to gravity g.

A person exerts a force of 38N on the end of a door 96cm wide. What is the magnitude of the torque if the force is exerted
(a) perpendicular to the door
and
(b) at a 60.0° angle to the face of the door?
*note: Please explain this in the simplest terms possible for me. Thank you so much :)

1. A person standing on the floor is leaning against a wall. The wall exerts on the person a force of 100 N in the horizontal direction. What other horizontal force keeps the person in equilibrium?
2. Torque is measured in Newton meters. Work can also be measured in Newton meters. What are the quantities measured in m

Equilibrium with torques on a ladder
A uniform ladder, length L= 4.5 m, and having mass M= 36 kg, leans against a frictionless wall with angle c= 50° above the floor. The coefficient of friction between ladder and floor is f=.55. A man whose weight is W= 480 newtons, climbs the ladder. Find the maximum distance d, that he can

A heavy pole, of mass M and length L, is freely hinged to a wall at the point O. A rope connects the other end of the pole, B, to a fixed point A on the wall above O. The system is in equilibrium, with the pole making an angle of θ with the horizontal, and the rope making an angle α with the horizontal... (i)Draw a for

Please see the attached file.
3. a 12 ft ladder that weighs 50 lb rests against a frictionless wall at a point 10 ft above the ground. How much force does the ladder exert (a) on the ground and (b) on the wall?

A machinist is using a wrench to loosen a nut. The wrench is 25.0 cm long, and he exerts a 17.0 N force at the end of the handle at 37 degrees (see attachment).
a) What is the magnitude of the torque does the machinist exert about the center of the nut?
b) What is the maximum torque he could exert with this force?

A 30.8 kg beam is attached to a wall with a hinge and its far end is supported by a cable. The angle between the beam and the cable is 90o. If the beam is inclined at an angle of q = 24.5o with respect to horizontal, what is the horizontal component of the force exerted by the hinge on the beam? (Use the `to the right' as + for

A force of 30N is applied perpendicularly to the face of a door at a distance of 1.5 m from the hinge of the door. Find the torque on the door about its hinge:
a. 20 n/m
b. 2nm
c. 45Nm
d. 20Nm

The figure shows a lower leg being exercised (see the attached file). It has a 49-N weight attached to the foot and is extended at an angle with respect to the vertical. Consider a rotational axis at the knee, as indicated. (a) When = 54°, find the magnitude of the torque that the weight creates. (b) At what angle does the m