课程名称：普通物理学甲 课程性质︰必修 课程教师︰陈凯风 开课学院：工学院 开课系所︰机械系 考试日期（年月日）︰2010/11/11 考试时限（分钟）：110分钟 是否需发放奖励金：是 1.Two cars move in the same direction. The position of the first car can be described by x=3t^2+2t+1(x,t in unit of meters,seconds);the acceleration of the second car is given by a=-4t(in m/s^2),and at t=0 ,its velocity is 8 m/s. When the velocities of these two cars match, and what is their velocity? [10 points] 2.The figure shows two blocks connected by a cord(of negligible mass)that passes over a frictionless pulley(also of negli gible mass).One block has mass m1;the other has mass m2. Assuming m2>m1, what is the tension in the cord?[10 points] ＿＿ ╱　　╲ 　　　　　　　　　　　　　∣滑 轮∣ ∣ ＿＿ ∣ ﹀ ﹀ ∣ ∣ ∣ ∣ m1 █ ∣ ▊m2 3.Following question 2, if the left block is actually a container, and it is losing mass(through a leak)at a constant rate R(in the unit of mass over time) .At what rate is the acceleration magnitude of the containers changing? i.e. da/dt=?[10 point] 4.A boy is initially seated on the top of a hemispherical ice mound of radius R. He begins to slide down the ice, with a negligible initial speed. Approximate the ice as being frictionless.At what height does the boy lose contact with the ice?[10 points] 5.The figure（一个圆心在(0,0)且半径为R的圆，挖掉一个边长为L的正方形，正方形 左下角座标为(0,0)shows a uniform metal plate of radius R, while a square of length L has been stamped out(removed)in an assambly line. (a)Using the x-y coordinate system shown,locate the center of mass of the remaining plate.[5 points] (b)what's the rotational inertia of the plate,if a rotational axis is assigned along the z axis and passing through the origin, if mass of the remaining plate is m?Some of the useful rotational inertias are given in page2.(这张 是HALLIDAY CH10里列出很多转动惯量的那张)[10 points] 6.Tap and the bathroom scale:aprecise scale(for measuring your body weight) is placed 1 meter under a tap.If the water flow of the tap is 300ml per second ,and the speed of water flow is 0.5m/s when the water leaves the tap. What is the measurement given by the scale,if the water hits the scale and stops immediateli?Given the free-fall acceleration g is 10m/s^2.[15 points] 7.Pitcher and catcher on boats: a pitcher stands in a boat,throws a baseball of mass m with speed v(relative to the pitcher)to the catcher on another boat;the catcher sends the ball back with a slower speed of v/2(relative to the catcher) to the pitcher.Assume the drag forcrs applying to the boats and the baseball are negligibly small,and the mass of the picher together with his boat is the same as the mass of the catcher and his boat(denoted by M).If they start this playing from rest,what is the speed of the pitcher after he caught the ball back?9[15points] 8.Two identicaltiny rockets of mass M at rest are binded to a steel thin rod of length L and mass m. The direction of the two rockets are oppositely arranged as the following figure.After firing the rockets,3/4 of the rocket masses are burned and exhaust products leave the rockets with a relative speed v. Find the final angular speed, treat the rockets as point-like objects. [15 points] M m 火 █───────█ 火 L M -------------------试题结束------------------ --

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