課程名稱︰普通物理學甲上 課程性質︰必修 課程教師︰王建萬 開課學院：工學院 開課系所︰工科海洋學系 考試日期（年月日）︰2009/11/13 10:20~12:10 考試時限（分鐘）：110 是否需發放獎勵金：是 （如未明確表示，則不予發放） 試題 : 09F Mid term Exam 1. The position "r" of a particle moving in an x-y plane is given by r=(4.00 t^4 - 4.00 t^2)i+(6.00 t - 5.00 t^3)j,with r in meters and t in seconds. In unit-vector notation,calculate (a) r (b) v ,and (c) a for t=2.00s (d) What is the angle between the positive direction of x-axis and a line tangent to the particle's path at t=2.00s. (e) What is the time that the particle has maximum horizontal range during 0 ≦ t ≦ 2.00 s. (10%) 2. A soccer player kicks a soccer ball of mass 0.50 kg that is initially at rest. The player's foot is in contact with the ball for 3.0 * 10^(-3) s, and the force of the kick is given by F(t) = [(7.0 * 10^6)t - (3.0 * 10^9)t^2] N for 0 ≦ t ≦ 3.0 * 10^(-3) s where t is in seconds. Find the magnitudes of (a) the impulse on the ball due to the kick, (b) the average force on the ball from the player's foot during the period of contact, (c) the maximum force on the ball from the player's foot during the period of contact,and (d) the ball's velocity immediately after it loses contact with the player's foot. (e) What is the average acceleration of the soccer ball during the kick? (10%) 3. A car travels at 100 km/h on a level road in the positive direction of an x-axis. Each tire has a diameter of 88cm. Relative to a woman riding in the car and in unit-vector notation, what are the velocity V at the (a) center, (b) top, and (c) bottom of each tire and the magnitude a of the acceleration at the (d) center, (e) top, and (f) bottom of each tire? Relative to a hitchhiker sitting next to the road and in unit-vector notation, what are the velocity V at the (g) center,(h) top, and (i) bottom of the tire and the magnitude a of the acceleration at the (j) center, (k) top, and (l) bottom of each tire? (18%) 4. In Fig.1, block 1 has mass m1=400g, block 2 has mass m2=800g,and the pulley which is mounted on a horizontal axle with negligible friction, has radius R = 6.00 cm. When released from rest, block 2 falls 80.0cm in 5.00s without the cord slipping on the pulley. (a) What is the magnitude of the acceleration of the blocks? What are (b) tension T1 and (c) tension T2 ? (d) What is the magnitude of the pulley's angular acceleration? (e) What is its rotational inertia? (f) What is the angular displacement of the pulley during 0 ≦ t ≦ 5.00 s (12%) ———————— ∣ ∣ ∣ R ∣ ∣ -——→∣ ∣ ∣ ∣ ∣ ———————— ∣ ∣ T1∣ ∣T2 ∣ ∣ ∣ ∣ ——— ——— m1∣ ∣ ∣ ∣m2 ∣ ∣ ∣ ∣ ——— ——— Fig. 1 5. In Fig. 2, a passenger of mass m = 60.0 kg stands on a platform scale in an elevator cab. We are concerned with the scale readings when the cab is stationary and when it is moving up or down. (a) Find a general solution for the scale reading, whatever the vertical motion of the cab. (b) What does the scale read if the cab is stationary or moving upward at a constant speed 0.60 m/s? (c) What does the scale read if the cab accelerates upward at 2.00 m/s^2 and downward at 2.00 m/s^2? (d) During the upward acceleration in part (c), what is the magnitude F(net) of the net force on the passenger, and (e) what is the magnitude a(p.cab) of his acceleration as measured in the frame of the cab? Does (f) F(net)=ma(p.cab)? (12 %) ——————— ∣ ∣ ∣ ∣ ∣ 人 ∣ ∣ ———— ∣ ∣ ∣ ∣∣ ——————— Fig. 2 6. Body A in Fig.3 weighs 160 N, and body B weighs 58 N. The coefficients of friction between A and the incline are μs = 0.56 and μk = 0.25 . Angle θ = 45。. Let the positive direction of an x-axis be up the incline. In unit-vector notation, what is the acceleration of A if A is initially (a) at rest, (b) moving up the incline, and (c) moving down the incline? (8 %) ＿＿＿＿ ／ ∣ ／ ／∣ ∣ A ／＼／ ／ ∣ ∣ ＼ ╲／ ∣ —— ＼／ ∣ ∣ ∣B ／ ∣ ∣ ∣ ／ ∣ —— ／θ ∣ ———————— Fig. 3 7. The block in Fig.4 lies on a horizontal frictionless surface, and the spring constant is 80 N/m. Initially, the spring is at its relaxed length and the block is stationary at position x = 0. Then an applied force with a constant magnitude of 5.0 N pulls the block in the positive direction of the x-axis, stretching the spring until the block stops. When that stopping point is reached, what are (a) the position of the block, (b) the work has done on the block by the applied force, and (c) the work that has been done on the block by the spring force? During the block's displacement, what are (d) the block's position when its kinetic energy is maximum and (e) the value of that maximum kinetic energy? (10%) x = 0 , F = 0 ∣ ＿ x ∣﹏﹏﹏﹏∣∣ Block attached to spring ∣ ∣∣ —————————— x ∣ Fig. 4 0 8. In Fig.5, a 70 kg rock climber is in a lie-back climb along a fissure, with hands pulling on one side of the fissure and feet pressed against the opposite side. The fissure has width w = 0.30 m, and the center of mass of the climber is a horizontal distance d = 0.45 m from the fissure. The coefficient of static friction between hands and rock is μ1 = 0.60, and between boots and rock is μ2 = 1.3 . (a) What is the least horizontal pull by the hands and push by the feet that will keep the climber stable? (b) For the horizontal pull of (a), what must be the vertical distance h between hands and feet? If the climber encounters wet rock, so that μ1 and μ2 are reduced, what happens to (c) the answer to (a) and (d) the answer to (b)? (10%) ∣ ∣ ∣ ∣ ＿ ∣ ∣ ∣∣ ∣ ∣ — ∣ w ∣ ∣∣ ————∣←→∣— ∣∣com ∣ ∣↑ ∣∣ .← —→∣ ∣ h ∣∣ d ∣ ∣ ∣∣ ∣ ∣↓ ————————— — Fig. 5 9. In Fig.6, a 4.0 kg block is accelerated from rest by a compressed spring of spring constant 520 N/m. The block leaves the spring at the spring's relaxed length and then travels over a horizontal floor with coefficient of kinetic friction μk = 0.30. The frictional force stops the block in distance D = 12.0 m. What are (a) the increase in thermal energy of the block-floor system, (b) the maximum kinetic energy of the block, (c) the original compression distance of the spring? (d) the speed and (e) the momentum of the block when it leaves the spring? (10 %) ∣ ＿＿＿＿ ∣ ∣ ∣ ∣﹏﹏﹏﹏﹏∣ ∣ ∣ ∣ ∣ ———————————————— ∣← No friction →∣← D →∣ (μk) Fig. 6 --

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