Spring 1 -­β 2018 General Physics 1 – Exam 1 Complete 6 out of 7 problems. If you choose to work out a 7th problem, it will count towards extra credit, which will be worth up to 10 points. 1. Position, Velocity, and Acceleration a) A baseball of mass 200 grams moves in 3D and its position vector (relative to the Earth’s surface) as a function of time is given by the following expression: π π‘ = 5π‘ ! ! + 10π‘ ! ! − 5 π meters π‘! Find the magnitude of the net force acting on the baseball at a time π‘ = 2 s. b) The velocity vs. time curve of a car traveling in 1D is shown in Figure 1. What is the net displacement of the car from the time π‘ = 0 s to π‘ = 6 s? 2. 1D Kinematics Consider two stones, A and B, one on either of your hands, held the same height over the edge of a cliff. Assume the water below is a very large distance away from where you hold the stones. See Figure 2. Initially stone A is thrown upward at 10 m/s. Two seconds later, stone B is thrown upward at 25 m/s. a) At what time, relative to the release of stone A, will the two stones have the same vertical location (besides at the very beginning of course)? b) At the moment indicated in part (a), find the velocity of each stone. Be sure to specify the direction of motion of each stone (up or down) at this same moment. 3. Vector Addition and Relative Velocities o a) Imagine you leave your tent at a camp site. You first walk 10 meters at 60 west of north, then you walk for 20 meters at 30o east of north, and finally walk for 10 more meters at 45o east of south. What is your overall displacement (give both magnitude and direction -­β above or below some axis)? b) See Figure 3. A plane intends to go directly across from point A to point B in the sky, however, there is wind blowing along a certain direction. Don’t assume that the wind is blowing purely east. The plane’s speed relative to the air is 500 km/h and is headed 30o west of north. The straight-­βline distance from point A to point B is 1,500 km, and you’re told the time of flight from A to B is 2 h. What is the magnitude of the wind velocity? You don’t have to convert the speeds into m/s . 4. 2D Projectile Motion A soccer ball is kicked from the ground level at an initial velocity of 30 m/s directed above the horizontal at an angle of 30° . See Figure 4. After some time from the kick, you are told that the ball is displaced horizontally by an amount of 50 m. a) What is the vertical displacement of the ball at the moment described? b) What is the instantaneous velocity (give magnitude and direction) at the moment described? 5. Forces I See Figure 5. Two blocks with masses π! = 10 kg and π! = 20 kg are connected by an inelastic, massless cord as a tension force ππππ is applied to the right of π! by the use of another inelastic, massless cord. The blocks are made of the same material. The coefficient of static friction between a block and the horizontal surface is π! = 0.50, and the coefficient of kinetic friction is π! = 0.25 . a) What is the minimum applied force that is required to begin moving the system of two blocks? b) If the force ππππ in magnitude is 200 N, determine the strength of the contact force between the two blocks. 6. Forces II See Figure 6. Two blocks with masses π! = 4 kg and π! = 2 kg are connected by a massless string that runs over a massless, sizeless pulley. The block of mass π! slides down along a frictionless incline and the block of mass π! slides horizontally along a frictionless surface. The angle of inclination is π = 60° . a) Find the magnitude of acceleration of the system. b) Find the tension in the string. 7. Forces III and Circular Motion a) See Figure 7. A small ball of mass π = 2 kg is attached to a massless string of length 5 cm and whirled about in a horizontal circle at a uniform rate. The angle that’s maintained between the vertical and the string is π = 30° . Find the period of revolution. b) See Figure 8. A backpack of mass π = 1 kg is suspended by two massless cords. The left cord makes an angle of 60° with the vertical, and the right string makes an angle of 45° with respect to the vertical. Find the tension on the left string. See next page for more information about resolving a vector in 3D space into its x, y, and z components.
