KEY & SOLUTIONS

1 PHYSICS worksheet STRESS, STRAIN, TENSION, COMPRESSION &ELASTICITY KEY & SOLUTIONS 22 Force of elasticity = StrainAreachange in dimension = Degree of Deformation = orginal dimension in Pa (unit of Pressure) 1 Pa = 1 N/mArea = r =StressFkxModulusStressStrainMeasured ==2 StressForce Maximum Stress = StrainMinimum AreaD () ** You NEED THIS FOR 2 problems2 StrainFLYALFFLAYLALLFS hear StressF hASxShearAxh == == == = 1. A spring is stretched m when a N weight is hung from it. What is the modulus for the spring? Data Equation Math Answer x = m F = N k = F x K = N/m 2. A spring is hanging empty at cm.

2 When 4 N are attached, it reaches to cm. What is the modulus for the spring? Data Equation Math Answer hi = m F = 4 N hf = k = F x x= |hf hi| x = | | = k = 4 N/m 3. What is the force needed to stretch a spring, with a k = 13 N/m a total of m? Data Equation Math Answer k = 13 N/m x = m F = kx F = 13 ( ) N 4. A spring has a k = 28 hangs at cm above the tabletop. How high above the table will the bottom of the spring be if N are applied to the spring? Data Equation Math Answer k = 28 hi = m F = N hf = |hi - x| x = F k x = 28 = hf = m 5. The bottom of a spring with a k = N/m is m above a tabletop when N are attached.

3 If the weight is removed, how far above the tabletop will the spring hang? Data Equation Math Answer k = N/m hf = m F = N hi = hf + x x = F k x = = hf = + m 6. A 250 g mass is hung from a spring that stretches from cm to cm. What is the k for the spring? Data Equation Math Answer m = kg hi = m hf = m k = F x x = |hf - hi| F = mg x = = F = ( ) = N k = N/m 7. A spring with a k = N/m hangs cm above a tabletop when a 400 g mass is hung from it. If the mass were removed, how far above the tabletop will be the bottom of the spring? Data Equation Math Answer k = N/m hf = m m = kg hi = hf + x x = F k F = mg F = ( ) = N x = = m hi = + m Or cm 8.

4 The heels on a pair of women s shoes have a radius of .5 cm at the bottom. If 30% of the weight of a woman 480N is supported by each heel, find the stress on each heel. Data Equation Math Answer F= = 480( ) = 144 N r = m Stress = F/A A = r2 A = ( ) ( )2 = x 10-5 Stress = 144 x 10-5 x 106 N/m2 9. Find the diameter of an 18 m (L) long steel wire that will stretch no more than m( L) when a load (stress) of 3800 N is hung on the end of the wire. The Young s Modulus for steel wire is 200 x 109 N/m2. Data Equation Math Answer L = 18 m L = m F = 3800 N Y = 200 x 109 N/m2 D = 2r = = =(3800)(18)(200 x 109 )( )= 10 5 = 10 10-3 D = 2( 10-3) m 10.

5 For safety in climbing mountaineers use a nylon rope that is 50 m long (L) and m in diameter. When supporting a 900 N climber the rope stretches m ( L) under tension. Find the Young s Modulus (Y) for the rope Data Equation Math Answer L = 50 m D = F = 900 N L = m = = 2 r = D/2 r = = A = ( )( )2 = x 10-5 =(900)(50)( x 10 5)( ) x 108 N/m2 11. The elastic limit of steel is Pa (N/m2), find the minimum diameter a steel wire can to support a 700 N weight without exceeding its elastic limit. Data Equation Math Answer Stressmax= Pa F = 700 N D = 2r = A = F/ Stressmax A = 700/5 = 140 m2 = 140 = D = 2( ) m 12. The distortion of the earth s crust is an example of sheer on a large scale.

6 A particular rock has a sheer modulus of x1010 Pa (N/m2)(Shear Modulus, S). What shear stress is applied when a 10 km layer (h) of rock is sheared a distance of 5 m ( x). Data Equation Math Answer S = x1010 Pa h = 10000 m x = 5 m = = 1010510000 x 106 N/m2 13. Human bone has a Young s Modulus of x108 N/m2(Y). Under compression, it can withstand a stress of about 160 x 106 N/m2(stress) before breaking. Assuming a human adult thigh bone (femur) is about .5 m (L) long, how much compression ( L) can the bone withstand before breaking. Data Equation Math Answer Y = x108 N/m2 Stress = 160 x 106 N/m2 L = m = =160 108 Or cm 14.

7 A cylindrical aluminum pillar high has a radius of cm. If a 2000-kg sculpture is placed on top of the pillar, by how much is the pillar compressed? Data Equation Math Answer h = m r = m m = 2000 kg YAl = 7 x 1010 = F = mg A = r2 A = ( )( )2 = m2 F = 2000 ( ) = 19600 N = (19600)(7)( )(7 1010) x 10-6 m 15. A mass of kg is supported by a copper wire of length m and diameter mm. Determine (a) the stress in the wire and (b) the elongation of the wire. Data Equation Math Answer m = kg L = m D = mm YCu = x 106 = F = mg Stress = F/A A = r2 r = D/2 r = /2 = 2 x10-3 A = ( )( 2 x10-3)2 = x 10-5 F = 2( ) = Stress = x 10-5 = x 10-4 = ( )(4)( 10 5)( 106) m 16.

8 A uniform pressure of 104 Pa is exerted on a copper block having a volume of 10 3 m3. What is the change in volume of the block? Data Equation Math Answer P = 104 Pa V0 = 10-3 m3 BCu = 11 x 1011 V= P/-B(Vo) V = ( 104)/( 11 x 1011)(10-3) x 10-10 m3 17. During a tensile strength experiment, a small-diameter fiber is elongated by a force of N. The fiber has an initial length of m and stretches a distance of 1024 m. The Young s modulus for the material being tested is 1010 Pa. Determine the diameter of the fiber. Data Equation Math Answer F = L = m L = 1024 m Y = 1010 Pa D = 2r = = = ( )( )( 1010)(4 1024)= 10 38 = 10 10 20 =2( ) x 10-19 m 18.

9 Determine the change in volume of a m3 block of granite when it is submerged about 3 km in the ocean, where the pressure on all surfaces is about 300 times ordinary atmospheric pressure of x 105 Pa. The bulk modulus of granite is 5x 10 Pa. Data Equation Math Answer V = 1 m3 P=(300)( ) = x 107 Pa B = 5 x 105 Pa = =( 107)(1)5 1010 x 10-4 m3 19. A m long steel piano wire has a diameter of cm. How great is the tension in the wire if it stretches cm when tightened? Young modulus for steel is x 1011 m/m2. Data Equation Math Answer L0 = m d = cm L = cm Y = 2 x 1011 N/m2 = A = r2 A = ( )( )2 = x 10-6 m2 =(2 10 11)(3. 14 10 6)( ) 981 N 20. A block of Jell-O is resting on a plate.

10 The Jell-O stands m tall and in the shape of a square that is m in length. You are bored, waiting for dinner and push tangentially across the top surface with a force of N. The top surface moves a distance of x = x 10-3 m relative to the bottom surface. What is the shear modulus of Jell-O? Data Equation Math Answer F = N L = H = m x = 6 x 10-3m = A = L x w A = ( )2 = x 10-3 m2 =( )( ) 10 3)(6 10 3) 460 N/m2 Or 460 Pa