1.060 Engineering Mechanics II Spring 2021
Problem Set 2
Due on Monday, February 27th
Important note: Please start a new sheet of paper for each problem in the
Problem
problem1 set. Write the names of the group members who contributed to the
solution at the beginning of each problem.
Figure 1: Dam in Problem 1.
You work in the quality control division for an engineering consulting firm. Your company
has been hired to design a concrete dam to aid in the creation of a new reservoir. A junior
consultant (an MIT grad) has submitted the final plans for the dam (See Figure 1). Your
job is to check to make sure that the dam is properly designed and will not topple over
about its pivot point A (it is assumed that the dam will not slide). In order to do this, you
need to figure out at what water depth (h) the dam will topple over. You are given the
following data: The depth of the river downstream of the dam is 10 m and is kept constant,
the density of the concrete is 2300 kg/m3, the height of the dam is 30 m, the base of the
dam is 15 m long, the dam and the reservoir are 100 m wide (into the page), and water
cannot leak under the base of the dam.
a) At what water depth h will the dam topple over about its pivot point A?
b) Is the dam properly designed?
2-1
, Problem 2
Figure 2: Gate in Problem 4.
A senior engineer (a Harvard grad) designed the gate in Figure 2. The gate consists of a
vertical section, AC, and an inclined section, CD, which are rigidly connected to each other
at C. The gate is hinged at D, and is kept in place by a single wire EC. Assume the gate to be
of 1 meter length into the plane of the paper. The weight of the gate is assumed negligible.
The gate ACD retains water, ρ = 1000 kg/m3, to its left. On the right of the gate, there is
air.
a) Sketch the pressure distribution along ACD and specify the values of the pressure at
points A, B, C, and D.
b) Determine the total pressure force acting on AC, FAC (magnitude, direction, line of
action).
c) Determine the total pressure force acting on CD, FCD (magnitude, direction, line of
action).
d) Determine the force exerted by the wire EC.
e) Determine the horizontal and vertical forces acting on the hinge at D.
2-2
Problem Set 2
Due on Monday, February 27th
Important note: Please start a new sheet of paper for each problem in the
Problem
problem1 set. Write the names of the group members who contributed to the
solution at the beginning of each problem.
Figure 1: Dam in Problem 1.
You work in the quality control division for an engineering consulting firm. Your company
has been hired to design a concrete dam to aid in the creation of a new reservoir. A junior
consultant (an MIT grad) has submitted the final plans for the dam (See Figure 1). Your
job is to check to make sure that the dam is properly designed and will not topple over
about its pivot point A (it is assumed that the dam will not slide). In order to do this, you
need to figure out at what water depth (h) the dam will topple over. You are given the
following data: The depth of the river downstream of the dam is 10 m and is kept constant,
the density of the concrete is 2300 kg/m3, the height of the dam is 30 m, the base of the
dam is 15 m long, the dam and the reservoir are 100 m wide (into the page), and water
cannot leak under the base of the dam.
a) At what water depth h will the dam topple over about its pivot point A?
b) Is the dam properly designed?
2-1
, Problem 2
Figure 2: Gate in Problem 4.
A senior engineer (a Harvard grad) designed the gate in Figure 2. The gate consists of a
vertical section, AC, and an inclined section, CD, which are rigidly connected to each other
at C. The gate is hinged at D, and is kept in place by a single wire EC. Assume the gate to be
of 1 meter length into the plane of the paper. The weight of the gate is assumed negligible.
The gate ACD retains water, ρ = 1000 kg/m3, to its left. On the right of the gate, there is
air.
a) Sketch the pressure distribution along ACD and specify the values of the pressure at
points A, B, C, and D.
b) Determine the total pressure force acting on AC, FAC (magnitude, direction, line of
action).
c) Determine the total pressure force acting on CD, FCD (magnitude, direction, line of
action).
d) Determine the force exerted by the wire EC.
e) Determine the horizontal and vertical forces acting on the hinge at D.
2-2
