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