Midterm I for phy231 Wednesday October 4 2000 Constants g 9 81 m s2 1 km 1000 m 1 A soccer ball is kicked and travels with a constant velocity of 79 2 km hr How long does it take to travel 11 m A 0 10 s B 0 14 s C 0 30 s D 0 40 s E 0 50 s Answer v 22 m s t xv 11 22 0 5 s 1 2 A ball is thrown up with an initial velocity of 28 m s What is its velocity after 4 s A 7 m s up B 7 m s down C 11 2 m s up D 11 2 m s down E 39 2 m s down Answer v vo at a g 9 81 m s2 v 11 2 m s 2 3 Three vectors of equal magnitude of 20 cm make angles of 90o 90o and 0o with respect to the x axis What is the length of the sum of these three vectors A 0 cm B 10 cm C 20 cm D 40 cm E 60 cm Answer The addition of the vectors at 90o and 90o gives zero So the total is just the third vector at 0o which has a length of 20 cm 3 4 A baseball after being struck with a bat is traveling in the air to the out eld Which statement is False Neglect air resistance A The acceleration is the same during the entire ight B The vertical speed is zero at the highest point of motion C The speed is least at the highest point of motion D As the ball is ascending its speed is decreasing E As the ball is descending its horizontal speed increases Answer E The horizontal speed is the same for the entire ight 4 5 A student playing darts aim his dart directly at a target on the same level 3 m away If the dart is released with a speed of 30 m s by how much will it miss the target A 0 049 m B 0 10 m C 0 20 m D 0 41 m E 0 51 m Answer x vt 0 1 s y 21 at2 0 049 with a g 5 6 A block of mass 20 kg sliding on a frictionless table is attached to another block of mass 10 kg by a string over a massless pulley as indicated What is the acceleration of the bigger mass in m s2 A 9 81 B 6 54 C 3 27 D 0 981 E 0 Answer Newton s second law for the hanging mass m1 is m1 g T m1a Newton s second law for the mass on the table m2 is T m2a solving for a gives a gm1 m1 m2 3 27 m s2 6 7 Tarzan nds himself stuck in the jungle from two vines as indicated in the adjoining sketch If his mass is 60 kg and the tension T is 600 N What is the angle in degrees A 2 9 B 5 7 C 29 3 D 45 0 E 78 5 Answer The component of the tension in the upward direction in each rope is T T sin The sum for the two ropes 2T must be equal to the weight force mg This means sin mg 2T 0 49 and 29 3o 0 0 7 8 A 180 N force accelerates a cart from 10 m s to 20 m s in 5 seconds What is the mass of the cart A 90 kg B 180 kg C 270 kg D 360 kg E 540 kg Answer v vo at to nd a v vo t 2 m s2 F ma to nd m F a 90 kg 8 9 What coe cient of kinetic friction is required to stop an object sliding on a at surface with a speed of 10 m s over a distance of 10 m A 0 35 B 0 51 C 0 71 D 0 89 E 1 96 Answer v 2 vo2 2ax with v 0 to nd a vo2 2x 5 m s2 The net force acting in the direction of motion is due to friction fk k mg Newton s second law is fk ma to nd k a g 0 51 9 10 A block of mass m slides on a frictionless inclined plane which makes an angle with the horizontal plane Which statement is False A The component of the gravity force parallel to the plane is mg sin B The component of the gravity force normal to the plane is mg cos C The reaction force of the plane is mg cos D The net force acting on the block is zero E The acceleration of the block depends on the angle Answer D The net force acting is mg sin 10 11 A roller coaster with mass 1000 kg starts at the top of a hill which is 100 m high Use energy conservation to nd the velocity at the bottom A 0 m s B 31 3 m s C 44 3 m s D 99 0 m s E 140 0 m s r Answer Energy conservation gives mgh mv v 2gh 44 3 m s 1 2 11 2 12 A car with mass 1500 kg starts from rest and accelerates with an average power output of 10 000 W Neglecting air resistance what is the speed of the car after 20 s A 2 6 m s B 3 6 m s C 5 7 m s D 11 5 m s E 16 3 m s Answer The total work input is W Pt and by energy conservation 1 2 this r is equal to the nal kinetic energy W 2 mv Thus v 2Pt m 16 3 m s 12 13 A person in a swing starts out from rest at a height of 3 0 meters above the ground What is the speed at the bottom of the arc which is 0 5 meters above the ground A 7 0 m s B 7 7 m s C 8 3 m s D 9 0 m s E 9 5 m s Answer The initial potential energy is PE1 mgh1 and the initial kinetic energy KE1 is zero The nal potential energy is PE2 mgh2 and the nal kinetic energy is rKE2 21 mv2 The sum KE PE is constant Solving for v gives v 2g h where h h1 h2 2 5 m Thus v 7 0 m s 13 14 A machine requires a power input of 1000 W After running for 20 s the useful energy output is 15 000 J What is the e ciency A 25 B 50 C 75 D 100 E 133 Answer e e ciency useful work total work input Work input is W Pt 20 000 J so e 15 000 20 000 75 14 15 A baseball with a mass of 0 20 kg is hit with an initial velocity of 10 0 m s Before it …
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