ENGR 127 Problem Set 1 Fall 2017

Due Date: August 30th (Sections 01-03 & 06) and August 31st (Sections 04-05) in Lecture

1)  Consider the case for the velocity of a vehicle during braking. The velocity is in one dimension with constant mass and constant breaking force resulting in a linear equation for velocity as a function of time.

a.  Setup: Describe the setup of this problem (e.g., include a diagram of the problem, a list of what is known/given and a list of what is being found).

b.  Calculation: Write the equation for the momentum balance for the time of the car’s negative acceleration, relating it to your diagram. Write the balance in terms of mass, velocity, acceleration and time variables. Clearly label the terms for initial momentum, change in momentum, and final momentum. Rearrange the above equation to show velocity as a function of time. Use variables for the constants, you will fit the constants in the next part.

c.  Calculation: Fit the constants in the linear equation using the data given in Table 1.

What do the constants in the equation represent physically?

d.  Graph: Sketch the graph of v(t), and clearly label the initial velocity, the acceleration, and the total stopping time on your graph.

2)  The spring force F and displacement x for a close-wound tension spring are measured as shown in Fig. 1. The spring force F and displacement x satisfy the linear equation F = k x + Fi, where k is the spring constant and Fi is the preload induced during manufacturing of the spring.

  1. Setup: Describe the setup of this problem (e.g., include a diagram of problem, a list of what is known/given and a list of what is being found).
  2. Calculation: Using the given data, find the equation of the line for the spring force F as a function of the displacement x, and determine the values of the spring constant k and preload Fi.
  3. Graph: Sketch the graph of F as a Function of x and clearly indicate both the spring constant k and preload Fi.

Figure 1: Close-wound tension spring. The included table shows
the spring length for two different forces.

3)  Calculation: The acceleration of the linear trajectory of a robot to pick up a part in a manufacturing process is shown in Figure 2. Determine the piecewise equation of a(t) for

(a) 0 ≤ t < 1 s

(b) 1 ≤ t 3 s

(c) 3 ≤ t 4 s

4)  Calculation: The velocity of the trajectory of a robot to pick up a part in a manufacturing process is shown in Figure 3. Determine the piecewise equation of v(t) for

(a) 0 ≤ t < 1 s

(b) 1 ≤ t < 3 s

(c) 3 ≤ t ≤ 4 s

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