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Charlie M.
Experienced ACT Tutor and Mechanical Engineering Student
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Physics (Thermodynamics)
TutorMe
Question:

A small dorm room refrigerator maintains an interior temperature of 5 degrees Celsius. The room temperature is 25 degrees Celsius. Assuming Carnot efficiency and a fully reversible system, determine the coefficient of performance (CoP) of the refrigerator.

Charlie M.
Answer:

The CoP is defined as Qc/Win. However, because the system is operating at Carnot efficiency, we can use the relative temperatures to determine the CoP (Qh/Th = Qc/Tc). Using this equation with the first law of thermodynamics Qin+Win=Qout+Wout + Estored we can simplify to CoP=Tc/(Th-Tc). Therefore CoP=13.9

Calculus
TutorMe
Question:

The area bounded by the line y=x^2 and x=1 is revolved about they positive y axis. Determine the volume (V) of this revolution without a calculator.

Charlie M.
Answer:

By using the washer method we can determine the volume by summing the area of washers with area A=pi(R^2-r^2) where R>=r and infinitely small height dy. To do so we must solve the first equation in terms of x. We get x=y^(1/2). We integrate the expression A*dy from y=0 to y=1 where R=1 and r=y^(1/2). Finally we get V=pi/2.

Physics
TutorMe
Question:

A small block rests on a rough wooden plank. Write an expression for the coefficient of static friction (mu) between the block and the plank in terms of the block mass (m), the plank mass (M), acceleration due to gravity (g), and the angle between the plank and the ground (theta) where theta is between 0 and 90 degrees (inclusive) and is the angle just before the block begins to slip.

Charlie M.
Answer:

From the problem statement we can conclude that the net force on the block is zero ("just before the block begins to slip"). Additionally, the force of friction is equal to the normal force (N) times the coefficient of static friction (mu). After summing the forces we come up with the expressions: N*mu=m*g*sin(theta) and N=m*g*cos(theta). After simplifying, we get m*g*cos(theta)*mu=m*g*sin(theta). Therefore mu = tan(theta).

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