3. ZAPIS OBLICZEŃ DO ĆWICZENIA .

s

sec 10

6

−

⋅

:=

i

1 8

..

:=

j

1 6

..

:=

k

1 6

..

:=

t1

i

167

μs

⋅

161

μs

⋅

167

μs

⋅

176

μs

⋅

168

μs

⋅

163

μs

⋅

156

μs

⋅

153

μs

⋅

:=

t2

i

124

μs

⋅

113

μs

⋅

144

μs

⋅

111

μs

⋅

147

μs

⋅

142

μs

⋅

121

μs

⋅

146

μs

⋅

:=

t3

i

135

μs

⋅

118

μs

⋅

135

μs

⋅

133

μs

⋅

129

μs

⋅

133

μs

⋅

134

μs

⋅

128

μs

⋅

:=

t4

i

131

μs

⋅

129

μs

⋅

123

μs

⋅

135

μs

⋅

139

μs

⋅

124

μs

⋅

131

μs

⋅

130

μs

⋅

:=

t5

i

125

μs

⋅

131

μs

⋅

127

μs

⋅

119

μs

⋅

122

μs

⋅

118

μs

⋅

120

μs

⋅

125

μs

⋅

:=

t6

i

114

μs

⋅

120

μs

⋅

119

μs

⋅

121

μs

⋅

126

μs

⋅

112

μs

⋅

112

μs

⋅

116

μs

⋅

:=

ϕ

k

3 deg

⋅

5 deg

⋅

7 deg

⋅

9 deg

⋅

11 deg

⋅

13 deg

⋅

:=

Średnie wartości czasu dla poszczególnych kątów

tsr

1

1

8

i

t1

i

∑

=

8

:=

tsr

2

1

8

i

t2

i

∑

=

8

:=

tsr

3

1

8

i

t3

i

∑

=

8

:=

tsr

4

1

8

i

t4

i

∑

=

8

:=

tsr

5

1

8

i

t5

i

∑

=

8

:=

tsr

6

1

8

i

t6

i

∑

=

8

:=

tsr

j

-4

1.639·10

-4

1.31·10

-4

1.306·10

-4

1.303·10

-4

1.234·10

-4

1.175·10

s

=

Wartości prędkości dla poszczegolnych kątów

g

9.81 m

⋅

sec

2

−

⋅

:=

l

45 cm

⋅

:=

v

k

2 g

⋅ l

⋅ 1

cos

ϕ

k

( )

(

)

−





⋅

:=

v

k

0.11

0.183

0.257

0.33

0.403

0.476

s

1

−

m

⋅

=

M

170 g

⋅

:=

R

35 mm

⋅

:=

E

20 10

10

⋅

N

⋅ m

2

−

⋅

:=

τ

k

M

2

E

2

R

⋅ v

k

⋅

















1

5

:=

τ

k

-3

1.784·10

-3

1.611·10

-3

1.506·10

-3

1.432·10

-3

1.376·10

-3

1.331·10

kg

0.4

−

s

0.2

m

0.4

⋅

⋅

=

Zależność ln(v) -ln(τ

τττ)

0.1

0.2

0.3

0.4

0.5

1.3 10

3

−

×

1.4 10

3

−

×

1.5 10

3

−

×

1.6 10

3

−

×

1.7 10

3

−

×

1.8 10

3

−

×

trace 1

Niepewności pomiarowe a i b:

a

6

1

6

j

v

j

tsr

j

⋅

(

)

∑

=

⋅

1

6

j

v

j

∑

=

1

6

j

tsr

j

∑

=

⋅

−

6

1

6

j

v

j

( )

2

∑

=

⋅

1

6

j

v

j

∑

=

















2

−

:=

b

1

6

1

6

j

tsr

j

∑

=

a

1

6

j

v

j

∑

=

⋅

−

















⋅

:=

a

9.969

−

10

5

−

×

s

2

m

1

−

⋅

=

b

1.62

10

4

−

×

s

=

ua

6

6

2

−

1

6

j

tsr

j

( )

2

∑

=

a

1

6

j

v

j

tsr

j

⋅

(

)

∑

=

⋅

−

b

1

6

j

tsr

j

∑

=

⋅

−

6

1

6

j

v

j

( )

2

∑

=

⋅

1

6

j

v

j

∑

=

















2

−

⋅

3.154

10

5

−

×

s

2

m

1

−

⋅

=

:=

ub

ua

1

6

1

6

j

v

j

( )

2

∑

=

⋅

⋅

1.005

10

5

−

×

s

=

:=