T = 2.34x10 6 s = 27.2days.

Transcription

1 Sole the following probles in the space proided Use the back of the page if needed Each proble is worth 10 points You ust show your work in a logical fashion starting with the correctly applied and clearly stated physical principles The equations you need are on the equation sheet Your score will be axiized if your work is easy to follow because partial credit will be awarded 1 Six different books slide off the edge of a table one at a tie The ass and speed along the table are gien Rank the books fro greatest to least based upon (a)the tie to hit the ground and (b)the horizontal distance fro the edge of the table to the point where the book lands You ust explain your reasoning for full credit A B C D E F 1kg 1/s 2kg 1/s 1kg 2/s 2kg 2/s 1kg 3/s 2kg 3/s (a)since the acceleration due graity is only ertical and does not depend upon ass, the horizontal otion does not affect the tie of fall So, A B C D E F (b)since the books all hae the sae tie to fall, the higher the horizontal elocity, the further they will trael in that tie So, E F > C D > A B 2 Use the data on the equation sheet to deterine (a)the force Earth exerts on the oon, (b)the force the oon exerts on the Earth, (c)the acceleration of the oon in its orbit around Earth, (d)the orbital speed of the oon, and (e)the period of the oon s orbit Gien: 736x10 22 kg, M 598x10 24 kg, and r 382x10 8 F E Find: F E?, F E?, a?,?, and T? (a)using the Law of Graitation, F E G M r 2 F E (667x10 11 ) (736x1022 )(598x10 24 ) (382x10 8 ) 2 F E 201x10 20 N (b)by Newton s Third Law these forces are equal and opposite So, F E 201x10 20 N in the direction shown (c)according to Newton s 2 nd Law, Σ F a a F E 201x x10 22 a s 2 (d)using the centripetal acceleration, a 2 (e)using the definition of speed, r ar (000273)(382x108 ) 1020 s x t 2πr T T 2πr 2π(382x108 ) T 234x10 6 s 272days 1020 r M F E 1

2 Physics 202A FINAL EXAM Chapters 1-15 Spring A 15kg box oes back and forth on a horizontal frictionless surface between two different springs, as shown The box is initially pressed against the spring on the left copressing it by 40c Then is released Find the axiu copression of the spring on the right k1 Gien: 15kg, x1 40c, k1 32N/c, and k2 16N/c Find: x2? x1 k2 x2 before after (a)the energy before is, K o 0 and U o U s 12 k1 x12 The energy after is, K 0 and U U s 12 k2 x22 Using the Law of Conseration of Energy, K o + U o K + U 12 k1 x12 12 k2 x22 x2 x1 x k1 k2 x2 57c 4 A 110kg astronaut heading to the right collides with and holds on to an 800kg astronaut oing upward After the collision, they oe off together at 220/s at an angle of 49 as shown Find the speed of each astronaut before the collision y 1 θ after x 2 before Gien: M 110kg, 800kg, 220/s, and θ 49 Find: 1? and 2? The initial oentu along each axis is px M1 and py 2 The final oentu along each axis is px (M + ) cosθ and py (M + )sin θ By the Law of Conseration of Moentu, the initial oentu along each axis is equal to the final oentu along each axis: M1 (M + ) cosθ and 2 (M + )sin θ Soling for the speeds and plugging in the nubers, 1 ( MM+ ) cosθ ( )(22)cos s 2 ( M + )sin θ ( )(22)sin s and 2

3 5 The airplane below traels horizontally staying at the sae altitude and speed as it flies by the tower The plane is shown at six different positions Rank these fro greatest to least based upon the planes (a)linear oentu, (b)kinetic energy, and (c)angular oentu You ust explain your reasoning for full credit (a)linear oentu is defined to be p Since the elocity and ass don t change, the linear oentu will stay the sae A B C D E F (b)kinetic energy is defined to be K Since the speed and ass don t change, the kinetic energy will stay the sae A B C D E F (c)angular oentu for a point particle is L r p r The elocity and ass don t change While r does ary, the part of r perpendicular to the elocity stays the sae A B C D E F 6 A 300-long diing board weighs 280N and is supported at a point 100 fro the end A dier weighing 500N stands at the free end Find the ertical force (agnitude and direction) at the (a)support point and (b)the left end d 1 y F s d 2 x Gien: F gb 280N, F g 500N, d 1 100, 300, and d Find: F s?, and? F gb F g )F gb d 2 F g 0 Applying the 2 nd Laws about the origin, ΣF y a y F s F gb F g 0 and Στ Iα d 1 ( d 2 1 Using the torque equation, 2 3 ( 1)F gb + d 2 F g ( 2 ) (500) 1140N d 1 1 Using the force equation, F s F gb + F g F s 1920N 3

4 7 A siple pendulu has a period of 160s on Earth Find the period of the pendulu on Mars where the acceleration due to graity is 371/s 2 Gien: T E 160s and 371/s 2 Find: T M? The angular frequency for a siple pendulu is, ω g The period is related to the angular frequency, ω 2π f 2π T 2π T 2π T ω g This is true for Earth and Mars, T M 2π T E 2π Plugging in the nubers, T M (16) T M T E T M 260s 8 The waes that are an earthquake hae a waelength of 13k and ibrate ten ties per inute Find (a)the frequency of the waes and (b)the speed of the waes Gien: λ 13k and f 100/in 0167Hz Find:? The speed is related to the waelength and frequency by, λ f (13)(0167) 22 k s 4

5 9 At the right are six objects that hae different asses and different olues These blocks are suspended at two different depths in water by a string fro a supporting rod Rank these situations, fro greatest to least, on the basis of buoyant force on the blocks by the water You ust explain your reasoning for full credit A B C D E F V 40 c 3 M 80 g V 40 c 3 V 10 c 3 According to Archiedes Principle, the buoyant force is equal to the weight of the displaced water The object with the biggest olue displaces the ost water V 10 c 3 M 80 g V 10 c 3 V 40 c 3 So, B D E > A C F 10 To ake soe instant coffee (yuck!) 400g of water ust be heated fro 200 C to 100 C (a)find the energy required (b)suppose you put in additional energy, describe what will happen Gien: 0400kg, c 4190J/(kg K), and T K Find: Q? (a)the quantity of heat is, Q c T (04)(4190)(80) Q 134x10 5 J (b)any additional heat will begin to boil the water and conert it to stea 5