大物期中考试

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UoG-UESTC Joint School of

University of Electronic Science and Technology of China

Physics I —Spring 2015 Mid-term Exam

10 May 2015

----------------------------------------------------------------------------------------------------------------------------------------------------------- Notice: Please make sure that both your UESTC and UoG Student IDs are written on the top of every sheet. This examination is closed-book and the use of a cell phone is not permitted. All scratch paper must be adequately labeled. Unless indicated otherwise, answers must be derived or explained clearly. Please write within the space given below on the answer sheets.

All questions are compulsory. There are 8 questions and a maximum of 100 marks in total. The following table is for grader only:

----------------------------------------------------------------------------------------------------------------------------------------------------------- Notice: All quantities in the questions are in SI units, and gravitational acceleration g =9.80m/s 2

Question 1 (10 points)

A particle moves in a straight line with acceleration a =6t 2

, it passes the origin with v =5m/s when t=1s. What is the motional

equation x (t)?

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Question 2

(10 points)

A car is running on a curved road. Its motional equation is expressed as 22()5cos 5sin

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t t r t i j =+

. (a) Prove that it is a circular motion. (b) Determine the tangential acceleration and radial acceleration.

Question 3 (10 points)

Three masses stay on a table with coefficient of friction

k μ, then start to move by a force F applied to m 1. Determine: (a) the

acceleration of the system; (b) the contact force that each mass applies on its neighbor.

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Question 4 (12 points)

A mass m slides down along a circular track (radius R ) from position A with no friction. When it arrives the position as figure,

determine (a) the magnitude of its acceleration; (b) the normal force acted by the track.

Question 5 (10 points)

(a) Particle A moves from x =0 to x =π/2 under force

2cos3F x =, determine the work done during the motion.

(b) Particle B moves from x =1 to x =-1 under force 3

234F x x

=-, determine the work done during the motion.

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Question 6

(15 points)

A block m =1kg is released from rest at point A on a track. Section A

B is 1/4 of a circle (radius R =2m) and is frictionless. BC

(length L =3m) is horizontal with a coefficient of kinetic friction 0.25k μ=, CD under the spring is also frictionless. Determine: (a) the velocity of block at point B; (b) the velocity of block at point C; (c) the maximum length of compression of the spring (k =600N/m).

Question 7 (16 points)

Consider a thin uniform semicircular plate with mass m and radius R . (a) Determine the CM (center of mass). (b) This object m

moves with initial velocity 1012v i j =-

, then collides on another resting object (mass M =2m ) and gives it a velocity 3M v i j =+ .

Determine the final speed of object m . (Ignore the external forces and all the motions are translational)

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Question 8 (17 points)

Two balls (same radius R but different mass) are connected by a uniform thin rod (M, l ). The system can rotate freely in the

vertical plane about the center of rod. Determine: (a) the rotational inertia; (b) the angular acceleration when the rod is horizontal; (c) the maximum angular velocity. (Rotational inertia of a ball about its center axis 22

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C I mR )