10. To find the RPM of the larger pulley, we can use the concept of belt speed, which remains constant for two pulleys connected by a belt.
The belt speed is given by the formula:
Belt Speed = Diameter of Pulley * RPM
Let's denote the RPM of the larger pulley as "x." Given that the diameter of the smaller pulley is 8 inches and its RPM is 100, we can set up the following equation:
8 inches * 100 RPM = 12 inches * x RPM
Simplifying the equation, we find:
800 = 12x
x = 66.67
Therefore, the larger pulley will make approximately 66.67 RPM.
11. To find the cost of 11 drills, we can use the concept of proportionality.
If 5 drills cost $3.15, we can set up the following proportion:
5 drills / $3.15 = 11 drills / x
Cross-multiplying and solving for x, we have:
5 * x = 11 * $3.15
x = (11 * $3.15) / 5
x = $6.93
Therefore, the cost of 11 drills is $6.93.
12. The taper of a plug is defined as the change in diameter per unit length. In this case, the taper is given as 1 inch over a length of 6 inches.
To calculate the taper per foot, we can convert the length to feet and then determine the change in diameter per foot.
1 inch taper / 6 inches length = x inch taper / 1 foot length
Cross-multiplying and solving for x, we have:
6 * x = 1
x = 1/6
Therefore, the taper per foot is 1/6 inch.
13. To find the diameter of the second pulley, we can use the concept of the speed ratio.
The speed ratio of two pulleys connected by a belt is given by the formula:
Speed Ratio = RPM1 / RPM2 = Diameter2 / Diameter1
Given that the diameter of the first pulley is 10 inches and its RPM is 120, and the RPM of the second pulley is 96, we can set up the following equation:
120 RPM / 96 RPM = Diameter2 / 10 inches
Cross-multiplying and solving for Diameter2, we have:
96 * Diameter2 = 120 * 10
Diameter2 = (120 * 10) / 96
Diameter2 ≈ 12.5 inches
Therefore, the diameter of the second pulley is approximately 12.5 inches.
14. Water pressure varies directly with the depth of the water. This means that the pressure increases linearly with depth.
If the total pressure on a certain area when submerged 15 feet is 75 lbs, we can set up a proportion to find the total pressure when submerged 80 feet.
15 feet / 75 lbs = 80 feet / x lbs
Cross-multiplying and solving for x, we have:
15 * x = 80 * 75
x = (80 * 75) / 15
x = 400 lbs
Therefore, the total pressure on the same area when submerged 80 feet would be 400 lbs.