合肥工业大学大学物理考试试题

Exercise:
1. A particle moving along x axis starts from x 0 with initial velocity v 0. Its acceleration can be expressed in a =-kv 2 where k is a known constant. Find its velocity function v =v (x ) with the coordinate x as variable.
2. A particle moves in xy plane with the motion function as
j t i t t r )3sin 5()3cos 5()(+=(all in SI). Find (a) its velocity )(t v and (b)
acceleration )(t a
in the unit-vector notation. (c) Show that v r ⊥. 3. A bullet of mass m is shot into a sand hill along a horizontal path, assume that the drag of the sand is kv f -=, find the velocity function v(t) if 0)0(v v = and the gravitation of the bullet can be
ignored.
4. what work is done by a conservative force j i x f 32+= that
moves a particle in xy plane from the initial position j i r i 32+= to
the final position j i r f 34--=. All quantities are in SI.
5. The angular position of a point on the rim of a rotating wheel is given by 320.30.4t t t +-=θ, where θ is in radians and t is in seconds. Find (a) its angular velocities at t=0s and t =4.0s? (b) Calculate its angular acceleration at t =2.0s. (c) Is its angular acceleration constant?
6. A uniform thin rod of mass M and length L can rotate freely about a horizontal axis passing through its top end o (23
1ML I =). A
bullet of mass m penetrates the rod passing its center of mass when the rod is in vertical stationary. If the path of the bullet is horizontal with an initial speed v o before penetration and 2
0v after penetration . Show that (a) the angular velocity of the rod just after the penetration is ML
mv 430=ω. (b) Find the maximum angular max θ the rod will swing upward after penetration.
7. A 1.0g bullet is fired into a block (M=0.50kg) that is mounted on the end of a rod (L=0.60m). The rotational inertia of the rod alone about A is 206.0m kg ⋅. The block-rod-bullet system then rotates about a fixed axis at point A. Assume the block is small enough to treat as a particle on the end of the rod. Question: (a) What is the rotational inertia of the block-rod-bullet system about A? (b) If the angular speed of the system about A just after the bullet ’s impact is 4.5rad/s , What is the speed of the bullet just before the impact? γ between the rest frame S and the frame S* in which the clock is rest. (b) what time does the clock read as it passes x =180m ?
9. What must be the momentum of a particle with mass m so that its total energy is 3 times rest energy?
10. Ideal gas within a closed chamber undergoes the cycle shown
the net energy added to the gas as heat shown in the Fig. temperature at state A is 300K.
(a). calculate the temperature of state B and C.
(b). what is the change in internal energy of the gas between state
A and state B? (int E ∆)
(c). the work done by the gas of the whole cycle .
(d). the net heat added to the gas during one complete cycle.
12. The motion of the electrons in metals is similar to the motion of molecules in the ideal gases. Its distribution function of speed is not Maxwell ’s curve but given by.
⎩
⎨⎧=0)(2Av v p the possible maximum speed v F is called Fermi speed. (a)。