The centripetal force is given by F = m v 2 r . The mass is measured to be 2 . 8 ± 0 . 1 k g , the velocity 14 ± 2 m / s and the radius 8 . 0 ± 0 . 2 m ; find the force on the mass, including the uncertainty.

Let's find determine F 0 F 0 = 2 . 8 k g × 14 m / s 2 8 m = 68 . 6 N Now, let's find the fractional uncertainty of the force, which can be found as follows ∆ F F 0 = ∆ m m + 2 × ∆ v v + ∆ r r = 0 . 1 2 . 8 + 2 × 2 14 + 0 . 2 8 = 0 . 346 Notice that ∆ F was approximated to one significant figure. Hence, F can be written as follows F = F 0 ± ∆ F = 68 . 6 N ± 20 N F ≈ 7 ± 2 × 10 1 N

The centripetal force is given by F = m v 2 r . The mass is measured to be 2 . 8 ± 0 . 1 k g , the velocity 14 ± 2 m / s and the radius 8 . 0 ± 0 . 2 m ; find the force on the mass, including the uncertainty.

Let's find determine F 0 F 0 = 2 . 8 k g × 14 m / s 2 8 m = 68 . 6 N Now, let's find the fractional uncertainty of the force, which can be found as follows ∆ F F 0 = ∆ m m + 2 × ∆ v v + ∆ r r = 0 . 1 2 . 8 + 2 × 2 14 + 0 . 2 8 = 0 . 346 Notice that ∆ F was approximated to one significant figure. Hence, F can be written as follows F = F 0 ± ∆ F = 68 . 6 N ± 20 N F ≈ 7 ± 2 × 10 1 N

The radius r of a circle is measured to be 2 . 4 c m ± 0 . 1 c m . Find the uncertainty in the area of the circle.

The area of the circle is described by the relation A = πr 2 , so let's first determine A 0 A 0 = π × ( 2 . 4 cm ) 2 = 18 . 096 cm 2 The fractional uncertainty of the area can be found as follows ∆ A A 0 = 2 × ∆ r r = 2 × 0 . 1 2 . 4 = 0 . 0833 ∆ A = A 0 × 0 . 0833 = 1 . 51 ≈ 2 c m 2 Notice that ∆ A was approximated to one significant figure. Hence , A can be written as follows A = A 0 ± ∆ A = 18 . 096 ± 2 c m 2 A ≈ 18 ± 2 c m 2

The radius r of a circle is measured to be 2 . 4 c m ± 0 . 1 c m . Find the uncertainty in circumference of the circle.

The circumference of the circle is described by the relation C = 2 πr , so let's first determine C 0 C 0 = 2 π × 2 . 4 cm = 15 . 08 cm The fractional uncertainty of the circumference can be found as follows ∆ C C 0 = ∆ r r = 0 . 1 2 . 4 = 0 . 0417 ∆ C = C 0 × 0 . 0417 = 0 . 628 ≈ 0 . 1 c m Notice that ∆ C was approximated to one significant figure. Hence, C can be written as follows C = C 0 ± ∆ C = ( 15 . 08 ± 1 ) c m C ≈ ( 15 ± 1 ) c m

The side of a rectangle are measured as 4 . 4 ± 0 . 2 c m and 8 . 5 ± 0 . 3 c m . Find the area and perimeter of the rectangle.

The area of the rectangle is described by the relation A = a × b , so let's first determine A 0 A 0 = 4 . 4 c m × 8 . 5 c m = 37 . 5 c m 2 The fractional uncertainty of the area can be found as follows ∆ A A 0 = ∆ a a + ∆ b b = 0 . 2 4 . 4 + 0 . 3 8 . 5 = 0 . 08075 ∆ A = A 0 × 0 . 08075 = 30 . 2 ≈ 3 c m 2 Notice that ∆ A Was approximated to one significant figure. Hence, A Can be written as follows A ≈ 37 ± 3 c m 2 The circumference of the rectangle is described by the relation C = 2 a + 2 b , so let's first determine C 0 , C 0 = 2 × ( 4 . 4 + 8 . 5 ) c m = 25 . 8 c m The fractional uncertainty of the circumference can be found as follows ∆ C = 2 ∆ a + 2 ∆ b = 2 × ( 0 . 2 + 0 . 3 ) c m C = C 0 ± ∆ C = 25 . 8 ± 1 c m

The volume of the cone of base radius R and height h is given by V = πR 2 h 3 . The uncertainty in the radius and in the height 4 % . Find the percentage uncertainty in the volume.

Notice that ∆ R R = ∆ V V = 4 % . Hence, we can write the fractional uncertainty of V as follows ∆ V V = 2 × ∆ R R + ∆ h h = ( 2 × 4 ) + 4 ∆ V V = 12 %

The following data was collected for current and voltage ( V , I ) = { ( 0 . 1 , 27 ) , ( 0 . 2 , 44 ) , ( 0 . 3 , 60 ) , ( 0 . 4 , 78 ) } With uncertainty of ± 4 m A in the current. Plot the current versus the voltage and draw the best-fit line. Suggest whether the current is proportional to the voltage.

As we can see from the graph, the line that has the best fit intersects the y-axis about 10 m A , which is clearly outside the uncertainty in the current, no straight line within the error bars can be made to pass through the origin unless a large systematic error in the current is made. The graph below describes a proportional relation between the current and the voltage, which is known as Ohm's law.

E M B I B E

Physics for the IB Diploma 6th Edition>Chapter 1 - Measurement and Uncertainties>Test yourself>Q 25

EASY

Diploma

IMPORTANT

Earn 100

The centripetal force is given by $F = \frac{m v^{2}}{r}$ . The mass is measured to be $2.8 \pm 0.1 k g$ , the velocity $14 \pm 2 m / s$ and the radius $8.0 \pm 0.2 m$ ; find the force on the mass, including the uncertainty.

Important Questions on Measurement and Uncertainties

EASY

Diploma

IMPORTANT

Physics for the IB Diploma 6th Edition>Chapter 1 - Measurement and Uncertainties>Test yourself>Q 26

The radius r of a circle is measured to be

2.4 c m \pm 0.1 c m

. Find the uncertainty in the area of the circle.

EASY

Diploma

IMPORTANT

Physics for the IB Diploma 6th Edition>Chapter 1 - Measurement and Uncertainties>Test yourself>Q 26

The radius r of a circle is measured to be

2.4 c m \pm 0.1 c m

. Find the uncertainty in circumference of the circle.

EASY

Diploma

IMPORTANT

Physics for the IB Diploma 6th Edition>Chapter 1 - Measurement and Uncertainties>Test yourself>Q 27

The side of a rectangle are measured as

4.4 \pm 0.2 c m

and

8.5 \pm 0.3 c m

. Find the area and perimeter of the rectangle.

EASY

Diploma

IMPORTANT

Physics for the IB Diploma 6th Edition>Chapter 1 - Measurement and Uncertainties>Test yourself>Q 28

The length

L

of a pendulum is increased by

2 %

. Find the percentage increase in the period

T .

EASY

Diploma

IMPORTANT

Physics for the IB Diploma 6th Edition>Chapter 1 - Measurement and Uncertainties>Test yourself>Q 29

The volume of the cone of base radius

R

and height

h

is given by

V = \frac{{πR}^{2} h}{3}

. The uncertainty in the radius and in the height

4 %

. Find the percentage uncertainty in the volume.

EASY

Diploma

IMPORTANT

Physics for the IB Diploma 6th Edition>Chapter 1 - Measurement and Uncertainties>Test yourself>Q 30

In an experiment to measure current and voltage across a device, the following data was collected

$(V, I) = {(0.1, 26),) (0.2, 48), (0.3, 65), (0.4, 90)}$ .

The current was measured in $m A$ And the voltage in $m V$ . The uncertainty in the current was $\pm 4 m A$ . Plot the current versus the voltage and draw the best-fit line through the points. Suggest whether the current is proportional to the voltage.

MEDIUM

Diploma

IMPORTANT

Physics for the IB Diploma 6th Edition>Chapter 1 - Measurement and Uncertainties>Test yourself>Q 31

The following data was collected for current and voltage

$(V, I) = {(0.1, 27), (0.2, 44), (0.3, 60), (0.4, 78)}$

With uncertainty of $\pm 4 m A$ in the current. Plot the current versus the voltage and draw the best-fit line. Suggest whether the current is proportional to the voltage.

EASY

Diploma

IMPORTANT

Physics for the IB Diploma 6th Edition>Chapter 1 - Measurement and Uncertainties>Test yourself>Q 32

A circle and a square have the same perimeter. Which shape has the larger area?