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a strong massless rope. The other end of the rope is attached to a steel water tank sitting on a flat horizontal concrete surface (see the image to the right). The coefficient of static friction between steel and concrete is 0.45 and the coefficient of kinetic friction between the surfaces is 0.30. The water tank, which is full of water, has sprung a leak. The combined mass of the water and the tank is 500 kg. This mass slowly decreases as the water leaks from the hole. You (i.e. your entire mass) are sitting at rest in the seat. You and the seat will remain at rest as long as the force of static friction is strong enough to hold you.
Task:
LET [DOWN] and [RIGHT] be positive. Using your knowledge of physics, determine the following:
Draw the FBD of the system of you and the chair while at rest. Using the LET statement above, write out the net force equation. [2]
Draw the FBD of the system of the water tank at rest on the flat horizontal surface. Using the LET statement above, write out the net force equations for both the vertical and horizontal planes. [3]
Using the net force equations, determine the minimum mass of water that must be lost (i.e. leaked out) from the water tank in order for you and the seat to begin falling? [4]
As soon as the chair begins to move, static friction between the steel tank and concrete surface becomes kinetic friction. Determine the magnitude of the kinetic friction. [3]
Using Newton’s 2nd law, determine the acceleration of the system at the instant that the static friction becomes kinetic friction. [6]

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hin a free demo session as I have my answers, but just want to confirm them, that would be greatly appreciated.
Question 1:
A block of mass M = 0.10 kg is attached to one end of a spring with spring constant k = 100 N/m . The other end of the spring is attached to a fixed wall. The block is pushed against the spring, compressing it a distance x = 0.04 m . The block is then released from rest, and the block-spring system travels along a horizontal, rough track. Data collected from a motion detector are used to create a graph of the kinetic energy K and spring potential energy Us of the system as a function of the block's position as the spring expands. How can the student determine the amount of mechanical energy dissipated by friction as the spring expanded to its natural spring length?
Question 2:
The Atwood’s machine shown consists of two blocks connected by a light string that passes over a pulley of negligible mass and negligible friction. The blocks are released from rest, and m2 is greater than m1. Assume that the reference line of zero gravitational potential energy is the floor. Which of the following best represents the total gravitational potential energy U and total kinetic energy K of the block-block-Earth system as a function of the height h of block m1?
Question 3:
A 2 kg block is placed at the top of an incline and released from rest near Earth’s surface and unknown distance H above the ground. The angle θ between the ground and the incline is also unknown. Frictional forces between the block and the incline are considered to be negligible. The block eventually slides to the bottom of the incline after 0.75 s. The block’s velocity v as a function of time t is shown in the graph starting from the instant it is released. How could a student use the graph to determine the total energy of the block-Earth system?
Question 4:
A block slides across a flat, horizontal surface to the right. For each choice, the arrows represent velocity vectors of the block at successive intervals of time. Which of the following diagrams represents the situation in which the block loses kinetic energy?

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aq) + 5 HBr (aq) ---> 3H2O (l) + 3Br2 (aq)

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units.
Chemical Equation: Write a generic chemical equation for the dehydration of cobalt (II) chloride ∙ x hydrate (include the state symbols of the reactant and two products). [T2]
Mass of Reactants and Products:
a) Calculate the initial mass of the hydrated cobalt (II) chloride. [T1]
b) Calculate the final mass of the anhydrous cobalt (II) chloride remaining in the cruiio8icible. [T1]
c) Calculate the mass of water given off by the sample of hydrated cobalt (II) chloride. [T1]
Moles of Products:
a) Calculate the moles of anhydrous cobalt (II) chloride remaining in the crucible. [T1]
b) Calculate the moles of water released from the hydrate. {T1]
4. Mole Ratio
a) Create an experimental mole ratio between the b) and a). [T1]
5. Formula of Hydrate: State the chemical formula you have determined for this hydrate.
Round the formula to the closest whole number value for x. [T1]
Discussion/Conclusion Questions: [T6]
Based on the chemical formula of the hydrate, calculate the percentage composition (percent by mass) of the hydrated cobalt (II) chloride. Remember to determine the percentage of each element (Co, Cl, H, and O). [T2]
A possible source of systematic error in this experiment is insufficient heating. Suppose that the hydrate was not completely converted to the anhydrous form. Describe how this would affect: the calculated percent by mass of water and the experimental molecular formula (i.e. would x be higher, lower or the same).
Suppose a student spilled some of the hydrated cobalt (II) chloride. Describe how this would affect the calculated percent by mass of water (would it be higher, lower or the same) and the experimental chemical formula of the hydrate. [T2]

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and 15.07 grams of CO2 and 6.170 grams of H2O are produced.
In a separate experiment, the molar mass is found to be 74.08 g/mol. Determine the empirical formula and the molecular formula of the organic compound.

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7.A 5kg mass is pushed by 2 forces horizontally( one 10N to the rigtht at a 53 degree, and the ...

n 4N to the left), and 1 vertical force(6N downwards).
Determine the net vertical force
Determine the magnitude and direction of the net force
Determine the acceleration of the mass

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9.An elevator WEIGHS 1.0 x 10⁴ N. {Part A} Draw a free body diagram for each part of this questions ...

to show which force is larger [5 marks] {Part B} Determine the MASS of the elevator [2 marks] {Part C} The elevator begins to accelerate UPWARDS from rest at 5.0 m/s². What is the force tension in the cable? [3 marks] {Part D} The same elevator is moving UPWARDS and starts to DECELERATE at 3.0 m/s². What is the force tension in the cable? [3 marks] {Part E} The elevator moves DOWN at CONSTANT velocity at 10 m/s. What is the force tension in the cable? [2 marks] {Part F} The elevator cable snaps (and everyone screams!). What are the forces working on the elevator now? Draw a diagram [2 marks]

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10.. A uniform cylinder of mass M and radius R is initially at rest on a rough horizontal surface. A ...

ght string is wrapped around the cylinder and is pulled straight up with a force T whose magnitude is 0.8 Mg. As a result, the cylinder slips and accelerates horizontally. The moment of
inertia of the cylinder is I = 12 MR2 and the coefficient of kinetic friction is 0.4.
a. On the diagram above show all the forces applied on the cylinder. b. Determine the linear acceleration a of the center of the cylinder. c. Determine the angular acceleration α of the cylinder.
d. Explain the difference in results of linear acceleration a and αR.

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1.AU MAT 120 Systems of Linear Equations and Inequalities Discussion

mathematicsalgebra Physics