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Young’s Modulus of a Cantilever
Aspect 1: Recording Raw Data TO 1 D.P.
Initial length: 82.1 cm ± 1mm
Weight (g)
±3% Length (cm)
± 3 mm % Error in Length
× 10-2 Extension (cm) Error in Extension (cm)
× 10-2
100
200
300
400
500
600
700
800
900
1000 78.1
74.3
70.5
66.8
63.1
59.5
56.4
52.9
50.2
47.4 ± 38.4
± 40.4
± 42.6
± 44.9
± 47.5
± 50.4
± 53.2
± 56.7
± 59.8
± 63.3 4.0
7.8
11.6
15.3
19.0
22.6
25.7
29.2
31.9
34.7 ± 1.5
± 3.2
± 4.9
± 6.9
± 9.0
± 11.4
± 13.7
± 16.6
± 19.1
± 22.0

Aspect 2: Processing the Data
Gradient = mass ÷ extension (sag)
Gradient= 480÷18
Gradient= 26.67
Error in gradient: (GMAX-GAVR) ÷ GAVR ×100
GMAX=29.6 GMIN=25.6 GAVR.= 26.6
(29.6-26.6) ÷26.6×100
Error in Gradient ≅ 11.3 ≅11%

Aspect 3: Presenting the Data

L- 82.1×10-2 m ± 0.1%(1×10-2m)

b- 2.85 × 10-2 m ± 4% (1×10-2m)

d- 0.6 × 10-3 m ± 8% ( 5×10-4 m)

g- 9.82 ms-2 (reference taken from physics teacher) s– Extension (sag)
M- Mass
g- acceleration of gravity
L- Length
E- Young’s Modulus of elasticity
b- Width
d- Thickness

s = 4MgL3 ÷ Ebd3
E = 4MgL3 ÷ bd3s
E = (4×9.82 ×(82.1×10-2) 3×M) ÷ ((2.85× 10-2)×(0.6× 10-3) 3×s)
E= (21.7) ÷((6.15× 10-9) × gradient)
E= 21.7÷ 1.64× 10-7
E=1.32 × 108 kg m-1 s-2 ± 5.15 × 107 kg m-1 s-2 Error in E= ((0.1×3)+4+(8×3)+11)
Error in E= 39%
Error in E= 5.15 × 107

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