HCI Worksheet 9 Forces and dynamics (answers)

Hwa Chong Institution Sec 3 Physics 1 Name: ________________________________________ Class: __________ Date: ___________ Sec 3 Physics Worksheet 9: Forces and Dynamics (Suggested Answers) SECTION A: CONCEPTUAL QUESTIONS 1 Can the velocity of an object reverse direction while maintaining a constant acceleration? If so, give an example; if not, explain. Yes. An object that is tossed upward in the air has a constant acceleration of g = 9.81 m s-2. I ts velocity keeps changing and eventually changes direction at the top of the trajectory. 2 Is it possible to move in a curved path in the absence of a force? Defend your answer. It is impossible to do so because Newton’s 1st law implies that all objects without a resultant force must travel in a straight line at a constant speed. Alternatively, you can think of an object moving in a curved path must have a constantly changing velocity because its direction component is changing. To change velocity requires acceleration. To have acceleration requires a force. 3 Three identical blocks are pulled as shown on a horizontal frictionless surface. If the tension in the rope held by the hand is 30 N, what is the tension in the other ropes? This question is very easy to solve if you have chosen the right system(s) to analyse. We can agree that all the blocks will have the same acceleration. Therefore, for the largest system, by Newton’s 2nd law, T0 = 3ma = 30 N [For the system of three blocks, all forces cancel out except for T 0. Therefore, ∑ 𝐹 = 𝑇0] Similarly, T1 = 2ma = 20 N [Inside the system (green dotted line), the mass = 2m while the only unbalanced force is T1.] and T2 = ma = 10N T1T2 T0 = 30 N m m m a T1T2

Hwa Chong Institution Sec 3 Physics 2 4 How does the force of gravity on a raindrop compare with the air drag it encounters when it falls at constant velocity? They are equal. 5 If you hold your book horizontally with a piece of paper beneath it, then drop both . They fall together. Repeat the experiment, but place the paper on top of the book. Describe the motion of the paper relative to the book. (Try it and see!) The book and the paper fall togeth er at the same rate. The surface area of the paper cannot be larger than that of the book. The book shielded the paper from the effects of air resistance. 6 How does the terminal speed of a parachutist before opening a parachute compare to terminal speed after? Why is there a difference? The terminal speed before opening the parachute is larger than after opening the parachute. When the parachute is first opened, the air resistance is greater than the weight , and so there is a resultant upward force, and the parachutist slows down. The magnitude of air resistance is dependent on the speed of the object . S o as the parachutist slows down, the air resistance due to the parachute decreases until it is finally equal to the weight. At that point, there is a new but lower terminal speed. 7 Why is it that a cat that accidentally falls from the top of a 50 -storey building hits a safety net below no faster than if it fell from the twentieth storey? The cat has reached terminal velocity by the time it has fallen 20-storey. 8 Under what conditions would a metal sphere dropping through a viscous liquid be in equilibrium? When the upward force s equal to the downward forces acting on the sphere. Upward forces are drag force and upthrust. The downward force is the weight. 9 If Galileo dropped two balls from the top of the Leaning Tower of Pisa, air resistance was not negligible. Assuming that both the balls were of the same size, one made of wood and one of iron, which ball hit the ground first? Why? The iron ball hits the ground first. The explanation is the same for the man and woman parachutists in Example 15. The iron ball has a greater weight, thus requiring a greater drag force to counter it. The reasoning is as follow: The drag forces on both balls start to increase during the fall. As the drag forces increase, it will come a time when the drag force on the wooden ball balances the wo oden ball’s weight first. At this time, the wooden ball reaches its terminal velocity. However, the drag force on the iron ball has yet to balance

Hwa Chong Institution Sec 3 Physics 3 SECTION B: MULTIPLE CHOICE QUESTIONS the iron ball’s weight and will continue to accelerate until eventually, it too is balanced by a greater drag force. The terminal velocity of the iron ball will be greater. 10 Free-fall is motion in which gravity is the only force acting. a Is a skydiver who has reached a terminal speed in free fall? No. Two forces are acting on him; the weight and the air drag. b Is a satellite above the atmosphere that circles the Earth in free fall? Yes. The satellite above the atmosphere has only one force acting on it; its weight , and therefore, it is indeed free -falling towards the Earth. Free falling does not mean that the object must fall vertically downward toward Earth. If it helps, you should know that the Moon is also free-falling toward Earth, and obviously, it doesn’t crash onto the Earth. 1 Three forces act on an object. If the object is in translational equilibrium, which of the following must be true? I The vector sum of the three forces must equal zero. II The magnitudes of the three forces must be equal. III All three forces must be parallel. A I only B II only C I and III only D II and III only E I, II, and III 2 A ball falls straight down through the air under the influence of gravity. There is a retarding force F on the ball with magnitude given by F = bv, where v is the speed of the ball and b is a positive constant. The magnitude of the acceleration a of the ball at any time is equal to which of the following? A gb− B bvg m− ( ) y F mg bv ma m g a bv bvga m bvag m = − =  − =  − =  = −  C bvg m+ D g b E bv m a bv mg

Hwa Chong Institution Sec 3 Physics 4 ( ) Consider the combined system as one body: 3 since the system goes with a cons tant acceleration 4 mg m m a ga =+ = 3 An object is released from rest on a planet that has no atmosphere. The object falls freely for 4.0 metres in the first two seconds. What is the magnitude of the acceleration due to gravity on the planet? ( )( ) 2 2 2 1 2 14 0 2.0 2 2.0 ms s ut at a a − =+ =+ = A 21.0 ms− B 22.0 ms− C 24.0 ms− D 28.0 ms− E 212.0 ms− 4 A block of mass 3m can move without friction on a horizontal table. This block is attached to another block of mass m by a cord that passes over a frictionless pulley. If the masses of the cord and the pulley are negligible, calculate the magnitude of the acceleration of t he descending block m? A zero B g/4 C g/3 D 2g/3 E g mg System = 3m + m blocks mg is the only unbalanced force in this system. Note: Many students will think that since the 3 m block offers no friction, the m block would be in free fall (or acceleration = g). This is not correct. While the 3m block does not provide friction, it provides resistance to motion due to inertia. For the same force, the greater mass experiences a lower acceleration.

Hwa Chong Institution Sec 3 Physics 5 5 An astronaut drops an apple on the surface of the Moon. The acceleration due to gravity is 1/6 on the Earth. The time it takes for the apple to fall to the ground compared with an apple dropped from the same height on the Earth is A the same B 6 times as long C 6 times as long D 36 times as long The following figure is used in questions 6 and 7. 6 A plane 5 metres in length is inclined at an angle of 37 , as shown above. A block of weight 20 newtons is placed at