Lab6_Centripetal_Force

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Eastern Kentucky University *

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101

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Mechanical Engineering

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Dec 6, 2023

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PHY 101 Lab 6: Centripetal Force Data Table 1 Trial W a s h e r s M a s s o f B a g w i t h W a s h e r s ( k g ) M as s of B o b be r (k g) R ad iu s ( m ) Circumfe rence (m) Tim e of 30 Rev olut ions (s) Ti m e of 1 Pe ri od (t) V e l o c i t y ( m / s ) V e l o c i t y 2 ( m 2 / s 2 ) Ce ntr ipe tal Fo rce (k g ⋅ m/ s 2 ) W e i g h t o f C y l i n d e r w i t h W a s h e r s Pe rce nt Dif fer en ce 1 1 0 . 0 0 6 0 . 0 0 2 0. 1 0.628 4.5 2. 2 5 0 . 2 7 9 0 . 7 7 9 0.0 49 0 . 0 7 4 1 0

7 2 2 0 . 0 1 3 4 0.002 0.1 0.628 3.8 1. 9 0 . 3 3 1 0 . 1 0 9 0.0 65 0 . 0 8 0 1 2 3 3 0 . 0 2 0 1 0.002 0.1 0.628 3.2 1. 6 0 . 3 9 3 0 . 1 5 4 0.0 88 0 . 0 8 7 1 4 4 4 0 . 0 2 6 8 0.002 0.1 0.628 2.7 1. 3 5 0 . 4 6 5 0 . 2 1 6 0.0 56 0 . 0 9 4 1 6 5 5 0 . 0 3 3 5 0.002 0.1 0.628 2.3 1. 1 5 0 . 5 4 6 0 . 2 9 8 0.0 81 0 . 1 0 0 1 8

1. In Activity 1, which way did the blue marble travel when the cup was removed? How does the velocity of the bobber when spun with a mass of 14 washers in the cylinder compare with the velocity of the bobber when spun with a mass of 8 washers in the cylinder? In Activity 1, the blue marble likely traveled outward or away from the center when the cup was removed. This is because the marble was in circular motion within the cup, and when the cup was lifted, the marble continued in a straight line due to its inertia. The velocity of the bobber when spun with a mass of 14 washers in the cylinder is likely to be higher than when turned with a mass of 8 washers. This is because the centripetal force required to keep the bobber in circular motion increases with greater mass, contributing to higher velocity. 2. Describe the relationship between the mass of the cylinder with the washers and the velocity of the bobber. There is a positive relationship between the mass of the cylinder with washers and the velocity of the bobber. As the mass of the cylinder (and consequently, the centripetal force) increases, the velocity of the bobber also increases. This relationship demonstrates that greater strength is required to maintain an object in circular motion with a larger mass. 3. What do you notice about the relationship between the centripetal force and the weight of the cylinder with washers? Explain the reason for this relationship. The centripetal force and the weight of the cylinder with washers should have a proportional relationship. As the importance of the cylinder (mass x gravitational acceleration) increases, the centripetal force required to keep the bobber in circular motion also increases. This relationship is because centripetal force is directly proportional to mass and the square

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of velocity (F_c = m * v^2 / r), and weight is directly proportional to mass (Weight = mass x gravitational acceleration). 4. How will centripetal force be affected if you double the velocity at which you spin the sphere? If you double the velocity at which you spin the sphere while keeping other factors constant (such as mass and radius), the centripetal force required will increase by a factor of four. Because centripetal force is proportional to the square of velocity (F_c = m * v^2 / r), doubling the rate will result in four times the centripetal force requirement. Increasing the velocity increases the force needed to maintain circular motion at a higher speed. 5. What would you expect to happen to the velocity of the bobber if the mass of the washers in the cylinder remained the same and the radius was doubled? If the mass of the washers in the cylinder remains the same, and the radius is doubled while keeping other factors constant, the velocity of the bobber would decrease. This is because the formula for centripetal force is: F_c = (m * v^2) / r Where:  F_c is the centripetal force required to keep the bobber in circular motion.  m is the mass of the bobber.  v is the velocity of the bobber.  r is the radius of the circular path. When the radius (r) is doubled, the denominator of the equation becomes more extensive, which means that to maintain the same centripetal force (assuming mass and velocity remain constant), the velocity (v) must decrease. So, in this scenario, if you double the radius while keeping the mass of the washers the same, the velocity of the bobber would decrease to maintain the balance between centripetal force and the other variables in the equation.