課程名稱︰普通物理學甲上
課程性質︰必修
課程教師︰蔡爾成
開課系所︰物理系開給大氣系
考試時間︰94/11/07
試題 :
(10% for each problem)
1.A block of mass M is pulled along a horizontal (*frictionless) surface by a
rope of mass m. A horizontal force F(->) acts on the rope.
(a) show that the rope must sag, even if only by an imperceptible amount.
Then, assuming the sag is negligible, find (b) the tension in the rope at its
midpoint.
2.A student want to determine the coefficients of static friction and kinetic
frinction between a box and a plank. She places the box on the plank and
gradually raises one end of the plank. When the angle of inclination with
horizontal reaches θ, the box starts to slip, and it then slides distance s
down the plank in time T at constant acceleration. What are the coeffcient of
static friction and the coefficient of kinetic friction between the box and
the plank.
3.After a completely inelastic collision, two objects of the same mass and
same initial speed are found to move away together at 1/2 their initial
speed. Find the angle between the initial velocities of the objects.
4.A rigid rod of length L and negligible mass has a ball with mass m attached
to one end and its other end fixed, to form a pendulum. The pendulum is
released at rest from horizontal position. At what angle from the vertical
does the tension in the rod is equal to weight of the ball?
5.How do we define the potential energy for a conservative force field such
that the sum of the kinetic energy and potential energy is a constant?
6.A paticle moves from (0.0.0) to (1,2,3) on a straight line. What's the work
done by the force field F(->) =xy i -z^2 j +7x^2 k on this particle?
(*i,j,k means unit vectors <1,0,0> <0,1,0> <0,0,1>)
7.What's the force field due to the potential energy field U(x,y,z)=xyz?
8.The total kinetic energy of a system of particles depends on the inertial
reference frame. Prove that the total kinetic energy is minimal in the
center of mass frame.
9.For the elastic collision of two particles observed in the center of mass
frame, show that the initial and final speed for each of two particles
remain same.
10.Two particles are of the same mass and one of them is at rest before
collision. Show that these two particles move in directions that are
perpendicular to each other after an elastic collision.
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