A 200-mL beaker that is half-filled with water is on the left pan of balance, and a sufficient amount of sand is placed on the right pan to bring the balance to equilibrium. A cube 4.0cm on an edge that is attached to a string is then lowered into the water until the cube is completely submerged, but not touching the bottom of the beaker. A piece of brass of mass m is then added to the right pan to restore equilibrium. What is m?

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Elin HesselLv2

17 Sep 2019

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An Iron ball suspended by a thread of negligible mass from an upright cylinder that floats partially submerged in water (so its basically an iron ball hanging from a string attached to a bottom of a soup can that is floating upright in water). The cylinder has a hieght of 6.00 cm, a face area of 12.0 cm^2 on the top and bottom, and a density of 0.30 g/cm^3, and 2.00 cm of its height is above the water surface. What is the radius of the iron ball?

A Simple Atwood Machine consists of two masses m1 and m1 that are connected by a string wound over a pulley, as seen in the figure below. m2 is larger than m1. On a piece of paper, draw two free body diagrams; one for each of the masses, showing all forces acting on each mass. Then answer the following questions. (a) Based on your free body diagram, identify the forces acting on the mass m1. Select all that apply. (m1+m2)a m1g FN m1a (m1+m2)g m2a f m2g T (b) Using the direction rosette indicate the direction for each of the forces acting on m1 that you identified in part (a). If any of the forces listed below is not applicable, enter NA. m1a= m2a= m1g= m2g= (m1+m2)a= (m1+m2)g= f= T= FN= (c) Based on your free body diagram, identify the forces acting on the mass m2. Select all that apply. T (m1+m2)g m2g m1g (m1+m2)a m1a m2a f FN (d) Using the direction rosette indicate the direction for each of the forces acting on m2 that you identified in part (c). If any of the forces listed below is not applicable, enter NA. m1a= m2a= m1g= m2g= (m1+m2)a= (m1+m2)g= f= T= FN= (e) Write Newton's Second Law equation (in the form Fnet = ma) for m1 in the y-direction. Use the first answer box for the left hand side (LHS) of the equation and the second answer box for the right hand side (RHS) of the equation. It is important to use the correct signs for each of the forces. Motion in the upward direction is positive and motion in the downward direction is negative. (Use m1, g, a, and T as appropriate.) LHS = RHS = (f) Write Newton's Second Law equation (in the form Fnet = ma) for m2 in the y-direction. Use the first answer box for the left hand side (LHS) of the equation and the second answer box for the right hand side (RHS) of the equation. It is important to use the correct signs for each of the forces. Motion in the upward direction is positive and motion in the downward direction is negative.(Use m2, g, a, and T as appropriate.) LHS = RHS = (g) Use your answers from parts (e) and (f) to get an expression for the magnitude of the tension T. (Use m1, m2, and g as appropriate.) magnitude of T = (h) Use your answers from parts (e), (f), and (g) to find the magnitude of a, the acceleration of the system. (Use m1, m2, and g as appropriate.) magnitude of a = (i) In what direction will each mass accelerate. For mass m1: For mass m2: (j) Suppose m1 = 7 kg and m2 = 11 kg. What is the tension in the string? T = (k) Suppose m1 = 7 kg and m2 = 11 kg. What is the value of the acceleration? a = (l) Suppose that m2 starts from rest at a height of 5 m. Use the Kinematic Equations to determine how long it takes for m2 to hit the ground.

Obtain an overflow can with a short metal tubeextendingoutward a bit below the top of the can. Place the overflowcan on alab jack set at its lowest position. Place a plastic beakernext tothe overflow can so that the plastic beaker will catch anywaterthat overflows. Fill the overflow can until waterstartsoverflowing into the plastic beaker, but donât let toomuchwater overflow. Once water has stopped overflowing carefullyremovethe plastic beaker making sure not to disturb the overflowcan andweigh the plastic beaker. Record the plastic beakerâsweightand then place it back beside the overflow can. (Recordweights asmass times g where mass is measured in kilograms and g =9.8m/s2.)

Mount a scale on top of a small ring stand. You should findacylindrical slot on the underside of the scale. Pick a metalblockof any material and hang it with a string (about 6 to 8incheslong) from the metal support at the bottom of the scale thatisdirectly connected to the scaleâs balance pan (the flathorizontalcircular surface where you usually place objects tomeasure theirmass). With the metal block hanging from the scaledetermine themass of the metal block by balancing the scale.

Carefully move the scale so the metal block is directlyoverthe overflow can and very slowly raise the lab jack so thatthemetal block becomes submerged. Water will overflow into theplasticbeaker. Once water has stopped overflowing re-weigh theplasticbeaker. Also, you will notice that the scale is no longerbalanced.Balance the scale to determine the apparent weight of themetalblock. This âweightâ is really equal to the actualweight minusthe buoyant force. From the change in weight of theblock calculatethe buoyant force. Also, from the change in weightof the plasticbeaker calculate the weight of the water displaced.Should theseweights be equal? Compare their values by calculatinga percentdifference.

In part I your instructor may have asked you to use agraduatedcylinder instead of the overflow can. Explain themeasurements thatyou made and how those measurements lead you toconclude thatArchimedesâ Principle is correct.

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