ESC-100 Quiz 1 Practice Problems

Significant figures & rounding

1. Indicate the number of significant figures for each of the following: a. 5.12500 b. 0.0204 c. 5.20 x 1013 d. 5 x 10-2

2. Write the following in scientific notation a. 0.030350 b. 390045

3. Solve the problems below with the correct significant figures a. 1 + 12 b. 414.92 – 14 c. 2222/2 d. 4.590 x 10-3 x 1.00 x 103

MATLAB

Write a short script that creates a matrix with 10 x 10 zeroes (100 zeroes total in a square matrix). If the rows are numbered from 1 – 10, have the script fill in each element with the value ((random number from 0 to 1) + x), where x is the number of the row the element is in. (Hint: use two for loops, one immediately within the other!)

Note that the command to return a random number between 0 and 1 is just “rand”.

Units/dimensional analysis

1. A particular type of ore contains 10 g gold per 1000 kg of ore. If gold is worth $400/ounce, what mass of ore must be mined to obtain gold worth $1,000,000 (Note that there are 16 ounces/lb, and 454 g/lb)?

2. A package of aluminum foil contains 100 ft2 of product and weighs approximately 1 lb. The density of aluminum is 2.70 g/cm3. Find the approximate thickness of the foil in mm. (Note that 3.28 ft = 1 m).

Estimation

Consider a cylindrical (volume = area * length) water jug with a diameter of 40 cm and a total volume of 100 L. If we consider the diameter of the earth to be 10,000 miles, about how many water jugs would it take to circle the earth end-to-end?

Arduino Example for ESC100 Quiz 1

Determine the following for the code and circuit shown (assume resistance and voltage values are good to three significant figures):

a) The voltage at pin A0 (with respect to ground).b) The status of the red led (on or off).c) The status of the yellow led (on or off).

int inputpin = 0; // analog pin used as inputint val; // variable to read the value from the analog pin int redLED=9; // pin for red LEDint yellowLED=10; // pin for yellow LEDvoid setup() { pinMode(redLED,OUTPUT); pinMode(yellowLED,OUTPUT);} void loop() { val = analogRead(inputpin); // reads the value of the input pin (value between 0 and 1023) if(val>300){ digitalWrite(redLED,HIGH); digitalWrite(yellowLED,LOW); } else{ digitalWrite(redLED,LOW); digitalWrite(yellowLED,HIGH); } }

A0

10

5V

GND

1000Ω 500Ω

330Ω

330Ω

Red

Yellow

Solution:• The voltage at A0 can be found by finding the current through the two resistors and then using

that current to find the voltage drop across the 500Ω resistor.• I=V/R=5.00V/1500Ω=3.33 mA• V=IR=(3.33mA)(500Ω)=1.67 Volts

• When this voltage is read in by analogRead(inputpin) the result will be (1.67V/5V)(1023)=341• 341>300 so the red LED will be on and the yellow LED will be off.

6 R.B. Bucinell Position, Distance, and Displacement Union College 2 August 2011

EXAMPLE PROBLEM

A radar station tracks an airplane by measuring the distance r to the airplane and the angle of elevation θ as shown in Figure 5. At a certain instant an airplane is sighted at r=4100m, θ=33.7°. After an interval of 0.75s the airplane is at r=4240m and θ=29.3°.

1. Draw a free body diagram for this problem. 2. Write the two positions of the plane in Cartesian vector form. 3. Determine the change in position vector, the displacement of the plane.

Figure 5: Illustration of the position of the airplane with respect to the radar station in the two positions discussed in the Example Problem.

7 R.B. Bucinell Position, Distance, and Displacement Union College 2 August 2011

SOLUTION

The position vectors for the plane in the two positions are written from the information given in the problem. The information is given in the magnitude-unit vector form, but needs to be converted to Cartesian form to facilitate subsequent calculations.

ˆ ˆ4240 cos 29.3 sin 29.3

ˆ ˆ ˆ4240 0.8721 0.4894

ˆ ˆ3698 2075

B

B rB

Bx By

r m i j

m i j r e

m i m j r r

(12)

ˆ ˆ4100 cos 33.7 sin 33.7

ˆ ˆ ˆ4100 0.8320 0.5548

ˆ ˆ3411 2275

A

A rA

Ax Ay

r m i j

m i j r e

m i m j r r

(13)

The change in the position or displacement of the airplane after the time interval is now calculated using vector mathematics and the Cartesian results in (12) and (13).

ˆ ˆ ˆ ˆ3698 2075 3411 2275

ˆ ˆ287 200

B Ar r r m i m j m i m j

m i m j

(14)

The displacement of the unit vector in Equation (14) can now be written in magnitude-unit vector form.

2 2287 200 349.8

ˆ ˆ287 200ˆ

349.8ˆ ˆ0.8204 0.5717

ˆ ˆ349.8 0.8204 0.5717

BA

r r m m m

r m i m je

r m

i j

r m i j

(15)

2 R.B. Bucinell Velocity Union College 3 August 2011

EXAMPLE PROBLEM

A radar station tracks an airplane by measuring the distance r to the airplane and the angle of elevation θ. At a certain instant an airplane is sighted at r=4100m, θ=33.7°. After an interval of 0.75s the airplane is at r=4240m and θ=29.3°.

1. Draw a free body diagram for this problem. 2. Write the two positions of the plane in Cartesian vector form. 3. Determine the change in position vector, the displacement of the plane.

3 R.B. Bucinell Velocity Union College 3 August 2011

SOLUTION

The position vectors for the plane in the two positions are written from the information given in the problem. The information is given in the magnitude-unit vector form, but is also converted to the Cartesian form to facilitate subsequent calculations.

ˆ ˆ4240 cos 29.3 sin 29.3

ˆ ˆ ˆ4100 0.8320 0.5548

ˆ ˆ3411 2275

B

B rB

Bx By

r m i j

m i j r e

m i m j r r

(2)

ˆ ˆ4240 cos 29.3 sin 29.3

ˆ ˆ ˆ4240 0.88721 0.7894

ˆ ˆ3698 2075

A

A rA

Ax Ay

r m i j

m i j r e

m i m j r r

(3)

The change in the position or displacement of the airplane after the time interval is now calculated using vector mathematics and the Cartesian results in (2) and (3).

ˆ ˆ ˆ ˆ3698 2075 3411 2275

ˆ ˆ287 200

B Ar r r m i m j m i m j

m i m j

(4)

The displacement of the unit vector in Equation (4) can now be written in magnitude-unit vector form.

2 2287 200 349.8

ˆ ˆ287 200ˆ

349.8ˆ ˆ0.8205 0.5718

ˆ ˆ349.8 0.8205 0.5718

BA

r r m m m

r m i m je

r m

i j

r m i j

(5)