### Fw: [试题] 100上 王名儒 普通物理学甲上 期中考

※ [本文转录自 NTU-Exam 看板 #1IQJ0QrY ]

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1. A grasshopper leaps upward, rising 0.4 meter in 0.2 xecond. How much
higher will it go ? Assuming the air effect is negligible and g = 10.0
m/sec^2.
2. A particle moves along the positive x-axis with x = 0 at t = 0. The x-t
plot in SI units shows a half circle with unit size. What is the acceleration
as a function of time for this particle ?
3. Find the work done by the force F(x,y) = xy^2 i+xy j along the line y = x
from point (0,0) to (2,2).
4. Derive the work-kinetic energy theorem W = ΔK by Newton's Law, where W is
the work done by the net force and K = 1/2mv^2 is the kinetic energy.
5. A 100 kg rock slides from rest down a hilliside that is 130 m long and
50 m high. The coefficient of kinetic friction between the rock and the
paved hill surface is 0.25. What is the speed of the rock as it reaches the
bottom of the hill ?
6. Following 5, if the rock has a spherical shape with 0.2 m in radius and is
rolling down, what will be the speed of the rock as it reaches the bottom of
the hill ?
7. Show that if a neutron is scattered through 90度 in an elastic collision
with an initially stationary deuteron in the Lab, frame, the neutron loses 2/3
of its initial kinetic energy to the deuteron. Note that m(deteron) =
m(neutron).
8. A large amount of ice with mass m around the South Pole melted and flew
into the ocean. Assuming that earth is a uniform sphere with radius R and
mass M, what will be the percentage change of the rotational speed of the
earth due to this melting ice effect ? Note that the rotational inertia is
2/3 MR^2 for a spherical shell and 2/5 MR^2 for a solid sphere.
9. Three bricks of length L, identical and uniform, are stacked on top of one
another in such a way that part of each extends beyond the one beneath. What
will be the maximum length of this stack assuming that the stack is kept in
equilibrium ?
10. A very massive star with mass M can collapse after burning its fuel out.
Make a rough estimate about the critical radius that when this star is small
than this size, no particles ( even photons ) can escape.

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