Explanation Given information: The weight of the space probe ( w ′ ) is 3,000 lb. The radius of gyration along x axis ( k x ) is 1.375 ft. The radius of gyration along y axis ( k y ) is 1.425 ft. The radius of gyration along z axis ( k z ) is 1.250 ft. The weight of the meteorite ( w ) is 5 oz. The velocity ( v 0 ) is ( 2400ft/s ) i − ( 3000ft/s ) j + ( 3200ft/s ) k . The width of the side panel from center to point A ( b ) is 9 ft. The length of the panel from center to point A ( l ) is 0.75 ft. Calculation: Calculate the mass of the space probe ( m ′ ) using the formula: w ′ = m ′ g m ′ = w ′ g Here, g is the acceleration due to gravity. Substitute 32 .2ft/s 2 for g and 3000 lb for w ′ . m ′ = 3000 32.2 = 93.17 lb ⋅ s 2 /ft Calculate the mass of the meteorite ( m ) using the formula: w = m g m = w g Substitute 32 .2ft/s 2 for g and 5 oz for w . m = 5oz× 1 16 lb oz 32.2 = 0.009705 lb ⋅ s 2 /ft Write the relative position vector ( r A ) at the point ( A ) of impact as follows: r A = b i + l k Substitute 9 ft for b and 0.75 ft. r A = ( 9 ft ) i + ( 0.75 ft ) k Calculate the initial liner momentum of the meteorite using the relation: Initial linear momentum = m v 0 Substitute 0.009705 lb ⋅ s 2 /ft for m and ( 2400ft/s ) i − ( 3000ft/s ) j + ( 3200ft/s ) k for v 0 . m v 0 = ( 0.009705 lb ⋅ s 2 /ft ) × ( 2400ft/s ) i − ( 3000ft/s ) j + ( 3200ft/s ) k = 23.292 i − 29.115 j + 31.056 k Calculate the moment about origin ( M O ) using the relation: M O = r A × m v 0 Substitute 23.292 i − 29.115 j + 31.056 k for m v 0 and ( 9 ft ) i + ( 0.75 ft ) k for r A . M O = | i j k 9 0 0.75 23.292 − 29.115 31.056 | = i [ ( 0 ) − ( − 21.836 ) ] − j [ ( 279.504 − 17.469 ) ] + k [ − 262.04 − 0 ] = 21.836 i − 262.04 j − 262.04 k Calculate the final liner momentum of the meteorite using the relation: Final linear momentum = 0.8 m v 0 Substitute 0.009705 lb ⋅ s 2 /ft for m and ( 2400ft/s ) i − ( 3000ft/s ) j + ( 3200ft/s ) k for v 0 . 0.8 m v 0 = 0.8 ( 0.009705 lb ⋅ s 2 /ft ) × ( 2400ft/s ) i − ( 3000ft/s ) j + ( 3200ft/s ) k = 18.634 i − 23.292 j + 24.845 k Calculate the final linear momentum of meteorite and its moment about the origin using the relation: M = r A × ( 0.8 m v 0 ) Substitute 18.634 i − 23.292 j + 24.845 k for 0.8 m v 0 and ( 9 ft ) i + ( 0.75 ft ) k for r A . M = | i j k 9 0 0.75 18.634 − 23.292 24.845 | = i [ ( 0 ) − ( − 17.469 ) ] − j [ ( 223.604 − 13.9755 ) ] + k [ − 209.63 − 0 ] = 17.469 i − 209.63 j − 209.63 k Write the expression for the conservation of angular momentum about the origin for a system of particles consisting of the probe plus the meteorite as follows: M O = H A + M H A = M O − M Here, H A is the angular momentum of the probe

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ISBN: 9781265566296

Author: BEER

Publisher: MCG

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Chapter 18.1, Problem 18.53P

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The kinetic energy (T′) of the space probe in its motion about its mass center after its collision with the meteorite.

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Chapter 18.1, Problem 18.52P

Chapter 18.1, Problem 18.54P

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180- Dimensions in mm 100 100 D E Steel B Brass 60 kN 40 kN 40-mm diam. 30-mm diam. PROBLEM 2.40 Solve Prob. 2.39, assuming that rod AC is made of brass and rod CE is made of steel. PROBLEM 2.39 Two cylindrical rods, one of steel and the other of brass, are joined at C and restrained by rigid supports at A and E. For the loading shown and knowing that E = 200 GPa and E, 105 GPa, determine (a) the reactions at A and E, (b) the deflection of point C. = R = 45.5 kN ← A

Dimensions in mm 100 100 -180- -120-+- C D Steel B Brass 60 kN 40 kN 40-mm diam. 30-mm diam. E PROBLEM 2.39 Two cylindrical rods, one of steel and the other of brass, are joined at Cand restrained by rigid supports at A and E. For the loading shown and knowing that E = 200 GPa and E₁ = 105 GPa, determine (a) the reactions at A and E, (b) the deflection of point C.

(read image) (Answer: vE = 0.514 m/s)

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The kinetic energy ( T ′ ) of the space probe in its motion about its mass center after its collision with the meteorite.

Solution Summary: The author calculates the kinetic energy of the space probe in its motion about its mass center after its collision with the meteorite.

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The kinetic energy (T′) of the space probe in its motion about its mass center after its collision with the meteorite.

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