This is a non-required review sheet for the beginning of second semester physics

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This is a non-required review sheet for the beginning of second semester physics. I would like answers just to double check that I have completed them all correctly. Thank you!

Considering the vectors: = 3x^ - 2^ and 2x^ - y^ Evaluate + Evaluate middot Evaluate - Evaluate times The displacement of a ball is expressed as: x(t)= -3t2 + 2t + 6 What is the ball's velocity as a function of time? What is the ball's maximum displacement? There are three forces acting on a crate: the first is N to the West and the second 30 N to the South. If the crate is not moving, what is the magnitude of the third force? A spherical asteroid of radius R has a density that varies with distance from its center: rho (r) = C/r Evaluate the mass dM of an infinitesimally thick spherical shell of radius r. Evaluate the total mass M of the entire asteroid. A satellite is orbiting the Earth with a radius of 7 times 106 m. Knowing that the mass of the Earth is about 6 times 1024 kg and the gravitational constant is G=6.67 times 10-11 Nm2/kg2, how fast is the satellite traveling? Calculate the gravitational flux Phi g, through an imaginary concentric spherical surface of radius r enclosing a planet of mass M, using the definition: Phi g = , where rho g(r) = GM/r2(- r^) What do you suspect the net flux might be if we instead used a cubic shape? Hint: Don't actually perform an integral... A force F = - b x2 x^ acts on a mass m. How much work must you perform to move it from: x = 0 to x=x0, at a constant value of y? y = 0 to y = y0, at a constant value of x ? x = 0, y = 0, along a diagonal path to x =0, y = y0? A mass m is attached to a spring with force constant k, where it is pulled a distanced away from equilibrium and then released. Use Newton's Second Law to write an equation of motion for the mass, and... Show that x(t) = A cos(omega t) is a valid description of the displacement of the mass. Show that the angular frequency of the mass' motion is omega = .

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This is a non-required review sheet for the beginning of second semester physics

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