Mechanical engineering

MAE 201 – Mechanics of Particles and Rigid Bodies I: Statics – Fall 2017 Homework #00

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Assignment: #0 Due: 4:00 PM, September 4th, 2017

Instructions: Complete all of the assigned problems. This homework assignment will be normalized to 10 points and will replace your Quiz 0 (the first day quiz) score if you had received 0 points for Quiz 0.

All solutions must use the seven-step problem setup process detailed in class. Failure to follow this process will result in a 0 for that problem. Remember that only variables are allowed in your schematics or FBDs – no numbers. Write N/A if a step does not apply to a particular problem (example, there may not be any assumptions if you are just computing the angle between two vectors, so Step 5 could read: 5) Assumptions: N/A)

Problem: 1. Find the length of side BC.

Problem: 2. To measure the length of a lake, a surveyor walks 245 yards from one end of the lake, turns 110º and then walks 270 yards until he arrives at the other end of the lake. What is the length of the lake?

Problem: 3. To measure the height of a tree, you walk North 100 ft from the base of the tree and measure the angle to the top of the tree to be 33º; however the trunk of the tree learning slightly away from you, tilted 9º away from you. How tall is the tree?

Problem: 4. (a) Determine the angle θ between the force F and line OA; (b) Determine the projected component of the force along the line OA.

Problem: 5. Three points A (1, 2, 3); B (1, 3, 2); C (3, 1, 2), determine a corresponding plane P. Find a vector N that is perpendicular to plane P.

Problem: 6. Let 𝐀 = 𝐴!𝐢 + 𝐴!𝐣 + 𝐴!𝐤 and 𝐁 = 𝐵!𝐢 + 𝐵!𝐣 + 𝐵!𝐤 be two non- collinear vectors. Show that the scalar triple product 𝐀 ⋅ 𝐀×𝐁 = 𝟎. Explain in words why this is.

Problem: 7. The projection of a vector B on vector 𝐀 = 2𝐢 + 𝐣 − 2𝐤 is 𝟏𝟑 𝟔 𝐀. If the

vector 𝐁 has magnitude 7 find the angle between 𝐀 and 𝐁.

Problem: 8. Block 1 is connected to Block 2 by a cable and is touching the angled wall with a dynamic friction, µ. Given an acceleration, a, and travel direction, v, find the mass, m2. Assume pulley is massless and frictionless. Let the θ, µ, m1, a, v, be as listed in figure.

! = 60.0˚ ( = 0.30 m1 = 12.0 kg v = 1.3 m/s a = 2.1 m/s²

!

m1 m2

av

Problem: 9. A block of mass, m, held by three, small, equal length cables with diameter, Dsmall. These cables are connected to a larger cable that is used to keep the entire mass spinning in a circle of radius, r, with an angular velocity, ω. The mass is 260 kg.

i) What is the tension, Tlarge, in the larger cable when the block as at the bottom of the circle as shown?

ii) What is the tension, Tlarge, in the larger cable when the block located is 180˚ from where it is shown (i.e., at the top of the circle)

r = 5.0 m ω = 2.21 rad/sec

(0.0, 0.0, 2.5)

(0.0, 0.0, 0.0)

(0.0, 1.0, 0.0)

(0.866, -0.5, 0.0)

Tlarge

(-0.866, -0.5, 0.0)

Dsmall cable

m = 260.0 kg

v

r

g