# Tutor profile: Daniel T.

## Questions

### Subject: Geology

You wish to determine the prehistoric location of Earth's Magnetic north pole. Explain in some detail how this can be done?

First, we must use some knowledge of paleomagnetics. We know that the direction of Earth's magnetic field is stored in Rock units along the seafloor. By taking a rock sample and dating it using an absolute dating method (such as carbon dating, or Argon-Argon dating) we can determine the age of the rock. Next, we can look at the direction of the magnetic dipoles inside the rock, to determine where they were pointing. This method can help us determine, and map out the precession of Earths magnetic north pole, at any point in time.

### Subject: Calculus

You wish to find the derivative of $$f(x) = x^{3} e^{2x}$$

In this case both terms $$x^{3}$$ and $$ e^{2x}$$ have an x in them. This means we must apply the product rule. The product rule states: derivative of first term $$\times$$ second term + Derivative of second term $$\times$$ first term Applying this formula we find: $$\frac{df}{dx} = 3x^{2} e^{2x} + 2e^{2x} x^{3}$$ we can simplify this by factoring out an $$x^{2}e^{2x}$$ giving a final answer of $$\frac{df}{dx} = x^{2}e^{2x}(3+2x)$$

### Subject: Physics

As part of your ninja training, you wish to determine the minimum amount of force required for you to pin a block of wood against a wall, without the block slipping downwards. Determine the forces acting on the block, and determine the relationship between them. Next calculate the force required (in Newtons) assuming the book has a mass of 1.5kg, and the coefficient of static friction between the block and the wall is 0.7.

First, we must draw a free body diagram to determine the forces acting on the block. In the y-direction (up and down) we have $$F_{G}$$ (gravity) pulling the block down, and $$F_{S}$$ (Static Friction) holding the block up. In the x-direction (horizontally) we have an applied force $$F_{A}$$, from the ninja pushing the block against the wall, and the normal force $$F_{N}$$ opposing the applied force. Now we can see this gives rise to two equations, In the x-direction $$F_{N} = F_{A}$$, and in the y-direction $$F_{S} = F_{G}$$ The question requires us to find an equation for $$F_{A}$$ since we want to determine the minimum amount of force required for the ninja to pin a block of wood against the wall. In order for the book to not fall we need friction (holding the book up) to be greater than or equal to gravity (pulling the book down), so we set: $$F_{S} = F_{G}$$ $$\mu \times F_{N} = m \times g$$ Where $$\mu$$ is the coefficient of friction, m is the mass of the block, and g is the acceleration due to gravity (9.81m/s). These are the basic equations for these forces. Next, we know that $$F_{N} = F_{A}$$ from above, so writing this in our equation gives: $$\mu \times F_{A} = m \times g$$ Then simply rearranging we find: $$F_{N} = \frac{m \times g}{\mu}$$ To calculate the force required in Newtons we plug in the numbers: $$F_{N} = \frac{m \times g}{\mu} = \frac{1.5 \times 9.81}{0.7} = 21N$$ The question is complete.

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