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159.100 Intro to Physics
. A stone of mass 52 g is resting on the ground. (a) List the forces acting on the stone. [1 mark] (b) State the magnitude and direction for each force identified in part (a). [1 mark] (c) By hand sketch a free body diagram of the stone while at rest on the ground. Include the net force on the stone. [2 marks] The stone is then picked up by a young child who then boards a hot-air balloon. Once the balloon is very high, the child drops the stone from the balloon. (d) By hand sketch a free body diagram of the stone the instant after it is released. Include the net force acting on the stone. [2 marks] (e) State the acceleration experienced by the stone at the instant after it is released. [1 mark] (f) At some instant during its fall, the stone is experiencing an acceleration of exactly 4.50 m s-2 downwards. Determine the friction (drag) force on the stone at that instant. [2 marks] (g) By hand sketch a free body diagram of the stone once it has reached terminal velocity. Include the net force acting on the stone. [2 marks] (h) State the acceleration experienced by the stone once it has reached terminal velocity. [1 mark] 2. A wooden box is at rest on a concrete ramp. The ramp is angled at 12◦to the horizontal. The box has a mass of 16 kg. The coefficient of friction between the wood and concrete is 0.62. (a) By hand draw a sketched diagram of the box on the ramp. Include and label all forces acting on the box. Do not include the net force. [2 marks] (b) By hand draw a free-body diagram of the box. Include and label all forces acting on the box. Do not include the net force. [1 marks] (c) Decompose the weight force vector into the component parallel to the ramp, FW‖ , and the component perpendicular to the ramp, FW⊥ . State the magnitude of these two vectors. [2 marks] (d) What is the magnitude of the normal force between the ramp and the box? [1 mark] (e) Calculate the maximum possible friction force acting on the box. [1 mark] 2 (f) What is the actual friction force acting on the box? [1 mark] (g) If your answers to the previous two questions are the same, why? If not, why not? [1 mark] The wooden box is now moved to a ramp that is identical except at an angle of 42◦. (h) What is maximum possible friction force on this new ramp? [2 marks] (i) Determine the acceleration of the box down the ramp when it is released. [2 marks] 3. An astronaut is in a spaceship at rest between two stars. To the left is a 2.56 ×1031 kg star, which is 1.25 ×107 km away. To the right is a star which is only 1.78 ×1029 kg but is also closer at 1.02 ×106 km away. Determine which star the ship will start to move toward. [3 marks] 4. Bob and Bill are on a beach. Bob has a 2.45 kg bag, and Bill has a 3.98 kg bag. They want to hang their bags off the ground, but all they have is a long, straight branch and a tall rock with a point to balance it on. Bob hangs his bag 1.25 m from the centre of the branch. The centre of the branch is directly on top of the tall rock. Where does bill need to place his bag? [2 marks] 5. A man is hunting using a rock attached to string as a type of sling. He swings the rock around above his head in a circle. When he lets go of the string, the rock flies towards his prey. (a) Explain how the tension and centripetal force relate to each other and to the rock’s motion. [2 marks] (b) If the rock has a mass of 210 g and constant speed of 15 m/s, and the string is 45 cm long, calculate the tension in the string. Ignore gravity. [2 marks] 6. Consider an elephant with a mass of 5.3 ×103 kg. Suppose its feet are approximately circular with a diameter of 42 cm. How much pressure does this elephant apply to the ground it is standing on? [3 marks] 7. Consider a woman wearing high-heeled shoes. By making (and clearly stating) a series of assumptions, estimate the pressure she applies to the floor she is standing on. (Clear explanation is required to gain full marks.
159.100 Intro to Physics
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