# Tutor profile: Mitchell W.

## Questions

### Subject: Physics (Newtonian Mechanics)

An object is sliding down a plane that is 10 degrees from horizontal, ignoring air resistance, what must the coefficient of friction be to keep the object at a constant velocity.

$$F_x=m*g*sin(10)$$ $$F_n=m*g*cos(10)$$ $$F_f=F_x=\mu*F_n$$ $$\mu=\frac{F_x}{F_n}=\frac{sin(10)}{cos(10)}=tan(10)=0.1763$$

### Subject: Nuclear Physics

How much energy is created when a deuterium atom and a tritium atom are fused into a Helium-4 atom and a neutron?

$$\Delta m= M(^2H)+M(^3H)-M(^4He)-M(^1n)$$ $$ = 2.014101+3.016049-4.002603-1.008665$$ $$=.01888208$$ amu $$E=\Delta m*c^2= 17.5887MeV$$

### Subject: Calculus

Determine the area of the region below the parametric curve given by the following set of parametric equations. You may assume that the curve traces out exactly once from right to left for the given range of t $$x=4t^3-t^2$$ $$y=t^4+2t^2$$ $$1<=t<=3$$

$$A=\int y dx = \int y\frac{dx}{dt} dt$$ $$A=\int_1^3 (t^4+2t^2)(12t^2-2t) = \int_1^3 12t^6 -2t^5 +24t^4-4t^3 dt$$ $$A=(\frac{12}{7}t^7- \frac{1}{3}t^6 +\frac{24}{5}t^5 -t^4 ) |_1^3 $$ $$A=4586.3619$$

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