PHY 121 Exam 1 Solutions Problem 1 2 5 points Answer on Scantron form A ball is dropped from the edge of a cliff Soon after a second ball is dropped As a function of time the separation between the two balls 1 stays the same 2 increases 3 decreases 4 it depends on the time specified Answer increases Problem 2 2 5 points Answer on Scantron form Two cars car A and car B start from rest and travel a distance d with constant accelera tion The acceleration of car B is four times that of car A After each car has traveled a distance d 1 car B is moving 16 times as fast as car A 2 car B is moving 8 times as fast as car A 3 car B is moving 4 times as fast as car A 4 car B is moving 2 times as fast as car A Answer car B is moving 2 times as fast as car A Problem 3 2 5 points Answer on Scantron form Two balls are projected off a cliff One is thrown horizontally while the other is released from rest and falls vertically Which of the following statements is true 1 The ball that falls vertically hits the ground first 2 The ball that is projected horizontally hits the ground first 3 Both balls hit the ground at the same time 4 We can not determine which ball hits the ground first unless we know the speed at which the first ball was projected horizontally Answer Both balls hit the ground at the same time Page 1 PHY 121 Exam 1 Solutions Problem 4 2 5 points Answer on Scantron form An elevator has a frayed cable which will break if the tension exceeds a certain value The tension is more likely to exceed this value if the elevator is Problem 5 2 5 points Answer on Scantron form A skier accelerates from rest on a slope inclined at an angle From this information we conclude that 1 moving at constant velocity 2 accelerating upward 3 accelerating downward 4 the motion is irrelevant Answer accelerating upward 1 k tan 2 k tan 3 k tan 4 k s Answer k tan Problem 6 2 5 points The time it takes for a falling object to attain its terminal velocity Answer on Scantron form 1 increases with increasing mass 2 decreases with increasing mass 3 is independent of mass Answer increases with increasing mass Page 2 PHY 121 Exam 1 Solutions Problem 7 2 5 points Answer on Scantron form Two blocks of the same size but different masses m1 and m2 are placed on a frictionless table side by side in contact with each other as shown in Fig 1 Assume that m1 m2 Figure 1 Masses m1 and m2 on a table Let N1 be the magnitude of the normal force between the two blocks when you push horizontally with a force F on the free side of m1 towards m2 Let N2 be the magnitude of the normal force between the two blocks when you push horizontally with a force F on the free side of m2 towards m1 Which of the following statements is true 1 N1 N2 2 N1 N2 3 N1 N2 Answer N1 N2 Page 3 PHY 121 Exam 1 Solutions Problem 8 2 5 points Answer on Scantron form A car travels along the x axis with increasing speed We are not sure if it is moving to the left or to the right Which of the graphs shown in Fig 2 could possibly represent the motion of the car Figure 2 The position x of the car as function of time 1 Graph a 2 Graph b 3 Graph c 4 Graph d 5 Graph e Answer Graph a Page 4 PHY 121 Exam 1 Solutions Problem 9 2 5 points Answer on Scantron form You measure the length of a plate using a ruler as shown in Fig 3 Figure 3 The measurement of the length of a plate What is your best estimate of the length of the plate in units of meters 1 10 0 10 5 m 2 10 5 11 0 m 3 11 0 11 5 m 4 11 5 12 0 m 5 12 0 12 5 m 6 12 5 13 0 m 7 13 0 13 5 m 8 13 5 14 0 m 9 14 0 14 5 m 10 14 5 15 0 m Answer 11 5 12 0 m Page 5 PHY 121 Exam 1 Solutions Problem 10 2 5 points Answer on Scantron form What must be the weather condition for the Dutch to hold the tegenwindfietsen race Hint see Fig 4 Figure 4 https www youtube com watch v VMinwf kRlA 1 Snowy 2 Rainy 3 Foggy 4 Windy 5 Very windy 6 Sunny 7 No special weather conditions are required Answer Very windy Page 6 PHY 121 Exam 1 Solutions Problem 11 25 points Answer in booklet 1 A ball of mass m is attached to a rigid vertical rod by means of two massless strings with length L The strings are attached to the rod at points a distance L apart as shown in Fig 5 The system is rotating about the axis of the rod both strings being taut and forming an equilateral triangle The tension in the upper string is T1 Figure 5 Configuration studied in Problem 11 a 5 points Draw a diagram showing all forces acting on the ball The forces acting on the ball are indicated Fig 6 The forces acting on the ball are a the tension T1 which is the force exerted by the upper string on the ball b the tension T2 which is the force exerted by the lower string on the ball c the weight W of the ball W mg We will use a coordinate system where the x axis is directed horizontally Nd the y axis vertically Page 7 PHY 121 Exam 1 Solutions Figure 6 Free body diagram of mass m b 5 points What is the tension in the lower string The ball is carrying out uniform circular motion in the horizontal plane This re quires that the net force along the vertical axis the y axis is zero Using Fig 6 we can write down the following expression for the net force along the y axis Using this equation we can obtain the following expression for T2 in terms of T1 Fy T1 sin30 T2 sin30 mg 0 T2 T1 mg sin30 T1 2mg c 5 points What is the net force on the ball at the instant shown in Fig 5 The net force acting on the ball is pointed horizontally towards the rotation axis and has a magnitude equal to Fr T1 cos30 T2 cos30 3 T1 T2 1 2 3 2T1 2mg 3 T1 mg 3 1 2 1 2 Page 8 PHY 121 Exam 1 Solutions d 10 points What is the speed of the ball If the ball carries out a uniform circular motion with velocity v and radius R there must …