Ch. 11: Some problems on density, pressure, etc.

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1 Q3 A pirate in a movie is carrying a chest (0.30 m 0.30 m 0.20 m) that is supposed to be filled with gold. To see how ridiculous this is, determine the mass (in kg) of the gold. Q15 A solid concrete block weighs 169 N and is resting on the ground. Its dimensions are m m m. A number of identical blocks are stacked on top of this one. What is the smallest number of whole blocks (including the one on the ground) that can be stacked so that their weight creates a pressure of at least two atmospheres on the ground beneath the first block? Q33 The hydraulic oil in a car lift has ρ = kg/m 3. The input piston s weight is negligible; the input piston & output plunger radii are m and m respectively. What input force F is needed to support the N combined weight of a car and the output plunger, when the bottom surface of the output plunger is (a) at the same level as the bottom surface of the input piston, and (b) 1.30 m above it? WORKED SOLUTIONS FOLLOW ONE-BY-ONE

2 Q3 A pirate in a movie is carrying a chest (0.30 m 0.30 m 0.20 m) that is supposed to be filled with gold. To see how ridiculous this is, determine the mass (in kg) of the gold.

3 Q3 A pirate in a movie is carrying a chest (0.30 m 0.30 m 0.20 m) that is supposed to be filled with gold. To see how ridiculous this is, determine the mass (in kg) of the gold. The question assumes (somewhat unrealistically) that the gold completely fills the chest. The calculation is therefore straightforward: 1. begin from the definition of density, and solve for m 2. substitute values ρ = m V m = ρv = ( kg.m 3 )(0.3 m 0.3 m 0.2 m) = 347 kg

4 Q15 A solid concrete block weighs 169 N and is resting on the ground. Its dimensions are m m m. A number of identical blocks are stacked on top of this one. What is the smallest number of whole blocks (including the one on the ground) that can be stacked so that their weight creates a pressure of at least two atmospheres on the ground beneath the first block?

5 Q15 A solid concrete block weighs 169 N and is resting on the ground. Its dimensions are m m m. A number of identical blocks are stacked on top of this one. What is the smallest number of whole blocks (including the one on the ground) that can be stacked so that their weight creates a pressure of at least two atmospheres on the ground beneath the first block? P = F/A = P is largest if A is smallest; turn each turn block so that area A = m m = m 2 stack of blocks sits on the ground in equilibrium like a single object: ΣF = ma = 0 = N = mg; Newton s 3rd = F block = N P > 2P atmos ; substitute for P, F/A > 2P atmos ; substitute for F, N.W block > 2P atmos.a; solve for no-of-blocks N, N > 2P atmos.a/w block ; = 2( Pa)(0.02 m 2 ) 169 N = The smallest number of blocks is 24 plug in values:

6 Q33 The hydraulic oil in a car lift has ρ = kg/m 3. The input piston s weight is negligible; the input piston & output plunger radii are m and m respectively. What input force F is needed to support the N combined weight of a car and the output plunger, when the bottom surface of the output plunger is (a) at the same level as the bottom surface of the input piston, and (b) 1.30 m above it?

7 Q33 The hydraulic oil in a car lift has ρ = kg/m 3. The input piston s weight is negligible; the input piston & output plunger radii are m and m respectively. What input force F is needed to support the N combined weight of a car and the output plunger, when the bottom surface of the output plunger is (a) at the same level as the bottom surface of the input piston, and (b) 1.30 m above it? (a) Pascal s principle: P transmitted throughout fluid and to the walls P input = P output ; substitute for P, F input /A input = F output /A output ; solve for F input, F input = F output = (24500 N) = 93.0 N (b) Try to do this part by yourself first... A input A output ; we need F output = W... π( m) 2 ; remember the squares!!! π(0.125 m) 2

8 Q33 The hydraulic oil in a car lift has ρ = kg/m 3. The input piston s weight is negligible; the input piston & output plunger radii are m and m respectively. What input force F is needed to support the N combined weight of a car and the output plunger, when the bottom surface of the output plunger is (a) at the same level as the bottom surface of the input piston, and (b) 1.30 m above it? (a) Pascal s principle: P transmitted throughout fluid and to the walls P input = P output ; F input = F output A input A output ; = N keeping extra digits for working... (b) We know how to relate the pressure at different depths in the fluid: P input = P output + ρgh; with a little working, F input = F output A input A output + A input ρgh; substituting, = (92.97 N) + π( m) 2 ( kg/m 3 )(9.8 ms 2 )(1.3 m) = 94.9 N

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