Uitwerkingen Week 1:
Opgaves: 11.1, 11.2, 11.3, 11.5, 11.6, 11.7, 11.18
11.1: Explain the function of each element of a computer-based instrumentation system:
Signal Conditioning transforms the changes in the electrical quantities into voltages, when
the electrical quantity is not a voltage.
11.2: Explain the basic concepts of sensors:
Sensor Collected analog signals
Sensor is a device that senses/detects specific physical property (pressure, temperature,
motion ect.) and produce related signal.
11.3: Select one: The relationship between pressure and force can be expressed as:
a) Pressure = Force X area
b) Pressure = Force/area
c) Force = pressure/area
d) None of above
11.4: Piezoelectric sensors can measure the pressure of the object according to the equation:
V0
P=
KEx
P = pressure in N/m2
x = displacement in meter
KE = voltage sensitivity of the sensor
Here, assume KE = 0,05 V · m/N. If an object is placed on the sensor, and measures V 0 = 2,8 V,
and x = 0,8 mm, then wat is the pressure form the object?
KE = 0,05 V· m/N
V0 = 2,8 V
x = 0,8 mm = 0,8 · 10-3
2,8
P=
0,05 · 0,8· 10−3
P = 70.000 Pa
11.5: What is Seeback effect?
The Seeback effect describes the generation of electricity following the connection of two
dissimilar electrical conductor or semiconductors that illustrate the thermoelectrical effect.
11.6: In figure which curve represents the characteristic of a thermistor?
,Curve: A
11.7: Which temperature sensors have a negative resistance temperature relationship?
a) Thermocouples
b) All RTD’s
c) Thermistors
d) Infrared thermometers
11.18: The resistance of an RTD is calculated with R RTD=R 0 [ 1+ α ( T −T 0 ) ] , and the coefficient
α = 0,004°C-1. The room temperature is (30˚C), R0 = 45 Ω. An RTD is put on a running CPU and
RRTD = 50 Ω. What is the surface temperature of the CPU?
R RTD
1+α ( T −T 0 ) =
R0
R RTD
α ( T −T 0 ) = −1
R0
RRTD
[ −1]
R0
( T −T 0 )= α
R RTD
[ −1]
R0
T= +T 0
α
50
[ −1]
45
T= +30
0,004
T=57,78˚C
,Uitwerkingen Week 2:
Opgaves: 11.9 t/m 11.13, 11.20
11.9: Which equation correctly expresses the acceleration?
dx
a) a=
dt
d2θ
b) ω= 2
dt
d2θ
c) α = 2
dt
d2 x
d)ω= 2
dt
11.10: An engineer designs a toy car. To measure the acceleration of this kind of toy car, he
also designs a simple accelerometer (a spring with spring constant 100 N/m and a mass m =
2kg) and binds it to the car. When the car is accelerated, he measures the displacement of
the mass which is 0,01m. What is the acceleration of the toy car?
K= 100N/m
m = 2 kg
x = 0,01m
K 100 m
a= · x a= ·0,01 a=0,5 2
m 2 s
11.1: Accelerometers are used widely in vehicles to decide whether safety air bags should be
deployed. Assume that the vehicle’s air bag is deployed when the seismic mass m for the
accelerometer is 0,22 kg and the vehicle’s acceleration is 145 m/s 2. If at this moment, the
mass displacement is measured as 0,025 m, then what is the spring constant for this
accelerometer?
m = 0,22 kg
a = 145 m/s2
x = 0,025 m
m·a 0,22· 145 N
K= K= K=1276
x 0,025 m
11.12: How is a Wheatstone bridge used to construct a load cell?
The Wheatstone bridge is also well suited for temp or load force with piezoelectric materials.
11.13: A load cell is constructed as a Wheatstone bridge. There is a linear relationship
between the output voltage Vo and the mass M, weighted: M = kVo + b, where k and b are
constant. The steady input voltage to the cell is Vi = 3,5 V and R1 = R2 = R3 = 220 Ω. To
calculate the value of k and b, two different masses (M1 = 1kg, M2 = 0,8kg) are loaded to the
cell, respectively, and the Rg is measured as 110 Ω and 130 Ω, respectively. Find k and b.
, M = kVo + b Vi = 3,5 V
k = constant R1 = R2 = R3 = 220 Ω
b = constant
M1 = 1 kg M2 = 0,8 kg
Rg = 110 Ω Rg = 130 Ω
R3 R2
V o=V i[ − ]
R 3+ R g R1 + R 2
For M1: For M2:
220 220 220 220
V o=3,5[ − ] V o=3,5[ − ]
220+110 220+220 220+130 220+220
V o=0,58 V V o=0,45 V
1 = 0,58k + b 0,8 = 0,45k + b
1 = 0,58k + b
0,8 = 0,45k + b -
0,2 = 0,13k
K = 1,54 kg/V
1 = 0,58 · 1,54 + b
b = 0,125 kg
11.20: A set of accelerators are installed on an object as shown in the figure below. Data are
collected from each accelerator from T = 0 s and T = 4 s, ax = 5 m/s2 and ay = 3 m/s2. Assume
the object is static at T = 0 s, calculate the object speed at T = 3 s.
∆ v=a·t
∆ v=15 m/ s
∆ v=9 m/ s
When using the Pythagorean theorem, the v can be calculated.
v = 17,5 m/s
Opgaves: 11.1, 11.2, 11.3, 11.5, 11.6, 11.7, 11.18
11.1: Explain the function of each element of a computer-based instrumentation system:
Signal Conditioning transforms the changes in the electrical quantities into voltages, when
the electrical quantity is not a voltage.
11.2: Explain the basic concepts of sensors:
Sensor Collected analog signals
Sensor is a device that senses/detects specific physical property (pressure, temperature,
motion ect.) and produce related signal.
11.3: Select one: The relationship between pressure and force can be expressed as:
a) Pressure = Force X area
b) Pressure = Force/area
c) Force = pressure/area
d) None of above
11.4: Piezoelectric sensors can measure the pressure of the object according to the equation:
V0
P=
KEx
P = pressure in N/m2
x = displacement in meter
KE = voltage sensitivity of the sensor
Here, assume KE = 0,05 V · m/N. If an object is placed on the sensor, and measures V 0 = 2,8 V,
and x = 0,8 mm, then wat is the pressure form the object?
KE = 0,05 V· m/N
V0 = 2,8 V
x = 0,8 mm = 0,8 · 10-3
2,8
P=
0,05 · 0,8· 10−3
P = 70.000 Pa
11.5: What is Seeback effect?
The Seeback effect describes the generation of electricity following the connection of two
dissimilar electrical conductor or semiconductors that illustrate the thermoelectrical effect.
11.6: In figure which curve represents the characteristic of a thermistor?
,Curve: A
11.7: Which temperature sensors have a negative resistance temperature relationship?
a) Thermocouples
b) All RTD’s
c) Thermistors
d) Infrared thermometers
11.18: The resistance of an RTD is calculated with R RTD=R 0 [ 1+ α ( T −T 0 ) ] , and the coefficient
α = 0,004°C-1. The room temperature is (30˚C), R0 = 45 Ω. An RTD is put on a running CPU and
RRTD = 50 Ω. What is the surface temperature of the CPU?
R RTD
1+α ( T −T 0 ) =
R0
R RTD
α ( T −T 0 ) = −1
R0
RRTD
[ −1]
R0
( T −T 0 )= α
R RTD
[ −1]
R0
T= +T 0
α
50
[ −1]
45
T= +30
0,004
T=57,78˚C
,Uitwerkingen Week 2:
Opgaves: 11.9 t/m 11.13, 11.20
11.9: Which equation correctly expresses the acceleration?
dx
a) a=
dt
d2θ
b) ω= 2
dt
d2θ
c) α = 2
dt
d2 x
d)ω= 2
dt
11.10: An engineer designs a toy car. To measure the acceleration of this kind of toy car, he
also designs a simple accelerometer (a spring with spring constant 100 N/m and a mass m =
2kg) and binds it to the car. When the car is accelerated, he measures the displacement of
the mass which is 0,01m. What is the acceleration of the toy car?
K= 100N/m
m = 2 kg
x = 0,01m
K 100 m
a= · x a= ·0,01 a=0,5 2
m 2 s
11.1: Accelerometers are used widely in vehicles to decide whether safety air bags should be
deployed. Assume that the vehicle’s air bag is deployed when the seismic mass m for the
accelerometer is 0,22 kg and the vehicle’s acceleration is 145 m/s 2. If at this moment, the
mass displacement is measured as 0,025 m, then what is the spring constant for this
accelerometer?
m = 0,22 kg
a = 145 m/s2
x = 0,025 m
m·a 0,22· 145 N
K= K= K=1276
x 0,025 m
11.12: How is a Wheatstone bridge used to construct a load cell?
The Wheatstone bridge is also well suited for temp or load force with piezoelectric materials.
11.13: A load cell is constructed as a Wheatstone bridge. There is a linear relationship
between the output voltage Vo and the mass M, weighted: M = kVo + b, where k and b are
constant. The steady input voltage to the cell is Vi = 3,5 V and R1 = R2 = R3 = 220 Ω. To
calculate the value of k and b, two different masses (M1 = 1kg, M2 = 0,8kg) are loaded to the
cell, respectively, and the Rg is measured as 110 Ω and 130 Ω, respectively. Find k and b.
, M = kVo + b Vi = 3,5 V
k = constant R1 = R2 = R3 = 220 Ω
b = constant
M1 = 1 kg M2 = 0,8 kg
Rg = 110 Ω Rg = 130 Ω
R3 R2
V o=V i[ − ]
R 3+ R g R1 + R 2
For M1: For M2:
220 220 220 220
V o=3,5[ − ] V o=3,5[ − ]
220+110 220+220 220+130 220+220
V o=0,58 V V o=0,45 V
1 = 0,58k + b 0,8 = 0,45k + b
1 = 0,58k + b
0,8 = 0,45k + b -
0,2 = 0,13k
K = 1,54 kg/V
1 = 0,58 · 1,54 + b
b = 0,125 kg
11.20: A set of accelerators are installed on an object as shown in the figure below. Data are
collected from each accelerator from T = 0 s and T = 4 s, ax = 5 m/s2 and ay = 3 m/s2. Assume
the object is static at T = 0 s, calculate the object speed at T = 3 s.
∆ v=a·t
∆ v=15 m/ s
∆ v=9 m/ s
When using the Pythagorean theorem, the v can be calculated.
v = 17,5 m/s
