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Tutor profile: Jordan M.

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Jordan M.
Physics PhD Student - Tutor and University Teaching Assistant of over 5 years.
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Questions

Subject: Physics (Newtonian Mechanics)

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Question:

A box of mass $$m$$ is compressing a horizontal spring with spring constant $$k$$ a distance of $$\Delta{x}$$. The spring decompresses, pushing the box across a surface with kinetic friction $$\mu_{k}$$. How far does the box slide beyond the point of the box's initial position before it returns to rest?

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Jordan M.
Answer:

Conservation of Energy. Potential energy in spring = work done by friction while sliding. $$mg\mu_{k}d = \frac{1}{2} k(\Delta x)^{2}$$ $$d = \frac{k (\Delta x)^{2}}{2mg\mu_{k}}$$

Subject: Calculus

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Question:

Differentiate the following functions with respect to x: 1. $$f(x) = 3x^{4} + x^{2} + 7$$ 2. $$g(x) = \sin(3x) + \cos(x+\pi)$$ 3. $$h(x) = \cos^{2}(3x) + \sin(x)\cos(2x)$$

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Jordan M.
Answer:

1. $$f'(x) = 12x^{3} + 2x$$ 2. $$g'(x) = 3\cos(3x) - \sin(x+\pi)$$ 3. $$h'(x) = -6\cos(3x)sin(3x) + \cos(x)\cos(2x) - 2\sin(x)\sin(2x) $$

Subject: Physics

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Question:

Suppose there is a truck of mass $$M$$ carrying a crate of mass $$m$$ in its bed. The truck is accelerating to the right (the positive x direction) through the force of friction exerted on the tires by the pavement below $$F_{drive}$$. The surface of the truck's bed has coefficients of static and kinetic friction $$\mu_{s}$$ and $$\mu_{k}$$, respectively. 1. What is the relationship between the magnitude of acceleration of the truck $$a_{truck}$$, the acceleration of the crate $$a_{crate}$$, and the acceleration of the system as a whole $$a_{sys}$$? 2. Draw free-body diagrams for the truck and the crate, identifying all relevant forces. Express their magnitudes in terms of the masses $$M, m$$, gravitational acceleration at Earth's surface $$g$$, and the coefficients of friction $$\mu_{s}, \mu_{k}$$. 2. Suppose that we do not know exactly what the coefficient of static friction on the truck's bed $$\mu_{s}$$ is. What is the minimum that it must be in order for it not to slide in the described situation? Express your answer in terms of the previously listed terms.

Inactive
Jordan M.
Answer:

1. $$a_{sys} = a_{truck} = a_{crate}$$ 2. Truck: $$\vec{F}_{net} = (F_{drive} - mg\mu_{s})\hat{i} + (Mg - (M+m)g)\hat{j}$$ Crate: $$\vec{F}_{net} = mg\mu_{s}\hat{i} + (mg - mg)\hat{j}$$ 3. $$\mu_{s} \geq \frac{a_{sys}}{g}$$

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