合肥工业大学大学物理考试试题.doc

Exercise:
1. A particle moving along x axis starts from x0 with initial velocity v0. Its acceleration can be expressed in a=-kv2 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 (all in SI). Find (a) its velocity and (b) accelerationin the unit-vector notation. (c) Show that.
3. A bullet of mass m is shot into a sand hill along a horizontal path, assume that the drag of the sand is , find the velocity function v(t) if and the gravitation of the bullet can be ignored.
4. what work is done by a conservative force that moves a particle in xy plane from the initial position to the final position . All quantities are in SI.
5. The angular position of a point on the rim of a rotating wheel is given by , where is in radians and t is in seconds. Find (a) its angular velocities at t=0s and t=? (b) Calculate its angular acceleration at t=. (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 (). A bullet of mass
m rates 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 vo before ration and after ration . Show that (a) the angular velocity of the rod just after the ratio