Grade 9 worksheet Chapter4 forces and the laws of motion Section1 changes in motion Summery : • Force is a vector quantity that causes acceleration (when unbalanced). • Force can act either through the physical contact of two objects (contact force) or at a distance (field force). • A free-body diagram shows only the forces that act on one object. These forces are the only ones that affect the motion of that object. Revision questions: 1. Is it possible for an object to be in motion if no net force is acting on it? Explain. 2. If an object is at rest, can we conclude that no external forces are acting on it? 3. An object thrown into the air stops at the highest point in its path. Is it in equilibrium at this point? Explain. 4. What physical quantity is a measure of the amount of inertia an object has? 5. Earth exerts a downward gravitational force of 8.9 N on a cake that is resting on a plate. The plate exerts a force of 11.0 N upward on the cake, and a knife exerts a downward force of 2.1 N on the cake. Draw a free-body diagram of the cake. 6. A chair is pushed forward with a force of 185 N. The gravitational force of Earth on the chair is 155 N downward, and the floor exerts a force of 155 N upward on the chair. Draw a free-body diagram showing the forces acting on the chair. 7. Draw a free-body diagram representing each of the following objects: a. a ball falling in the presence of air resistance b. a helicopter lifting off a landing pad c. an athlete running along a horizontal track 8. Four forces act on a hot-air balloon, shown from the side in the figure below. Find the magnitude and direction of the resultant force on the balloon. 9. Two lifeguards pull on ropes attached to a raft. If they pull in the same direction, the raft experiences a net force of 334 N to the right. If they pull in opposite directions, the raft experiences a net force of 106 N to the left. a. Draw a free-body diagram representing the raft for each situation. b. Find the force exerted by each lifeguard on the raft for each situation. (Disregard any other forces acting on the raft.) 10. A dog pulls on a pillow with a force of 5 N at an angle of 37° above the horizontal. Find the x and y components of this force. Section2 newtons first law Summery : • The tendency of an object not to accelerate is called inertia. Mass is the physical quantity used to measure inertia. • The net force acting on an object is the vector sum of all external forces acting on the object. An object is in a state of equilibrium when the net force acting on the object is zero. Revision questions : 1. A flying, stationary kite is acted on by a force of 9.8 N downward. The wind exerts a force of 45 N at an angle of 50.0° above the horizontal. Find the force that the string exerts on the kite. Section3 newtons second and third law Summery : • The net force acting on an object is equal to the product of the object’s mass and the object’s acceleration. • When two bodies exert force on each other, the forces are equal in magnitude and opposite in direction. These forces are called an action-reaction pair. Forces always exist in such pairs. Revision questions: 1. Space-shuttle astronauts experience accelerations of about 35 m/s2 during takeoff. What force does a 75-kg astronaut experience during an acceleration of this magnitude? 2. An 8.5-kg bowling ball initially at rest is dropped from the top of an 11-m building. The ball hits the ground 1.5 s later. Find the net force on the falling ball. 3. The force that attracts Earth to an object is equal to and opposite the force that Earth exerts on the object. Explain why Earth’s acceleration is not equal to and opposite the object’s acceleration. 4. State Newton’s second law in your own words. 5. An 1850 kg car is moving to the right at a constant speed of 1.44 m/s. a. What is the net force on the car? b. What would be the net force on the car if it were moving to the left? 6. What acceleration will you give to a 24.3 kg box if you push it horizontally with a net force of 85.5 N? 7. What net force is required to give a 25 kg suitcase an acceleration of 2.2 m/s2 to the right? 8. Two forces are applied to a car in an effort to accelerate it, as shown below. a. What is the resultant of these two forces? b. If the car has a mass of 3200 kg, what acceleration does it have? (Disregard friction.) Section4 every day forces Summery : • The weight of an object is the magnitude of the gravitational force on the object and is equal to the object’s mass times the acceleration due to gravity. • A normal force is a force that acts on an object in a direction perpendicular to the surface of contact. • Friction is a resistive force that acts in a direction opposite to the direction of the relative motion of two contacting surfaces. The force of friction between two surfaces is proportional to the normal force. Revision questions: 1. Do the forces in Figure constitute an action-reaction pair (Newton’s third law)? 2. A refrigerator is placed on a ramp. The refrigerator begins to slide when the ramp is raised to an angle of 34°. What is the coefficient of static friction? 3. Explain the relationship between mass and weight. 4. A 0.150 kg baseball is thrown upward with an initial speed of 20.0 m/s. a. What is the force on the ball when it reaches half of its maximum height? (Disregard air resistance.) b. What is the force on the ball when it reaches its peak? 5. Draw free-body diagrams showing the weight and normal forces on a laundry basket in each of the following situations: a. at rest on a horizontal surface b. at rest on a ramp inclined 12° above the horizontal c. at rest on a ramp inclined 25° above the horizontal d. at rest on a ramp inclined 45° above the horizontal 6. If the basket in q-5 has a mass of 5.5 kg, find the magnitude of the normal force for the situations described in (a) through (d). Chapter5 ( work and energy ) Section1 work Summery : • Work is done on an object only when a net force acts on the object to displace it in the direction of a component of the net force. • The amount of work done on an object by a force is equal to the component of the force along the direction of motion times the distance the object moves. Revision questions: 1. A 20.0 kg suitcase is raised 3.0 m above a platform by a conveyor belt. How much work is done on the suitcase? 2. Discuss whether any work is being done by each of the following agents and, if so, whether the work is positive or negative. a. a chicken scratching the ground b. a person reading a sign c. a crane lifting a bucket of concrete d. the force of gravity on the bucket in (c) 3. A person lifts a 4.5 kg cement block a vertical distance of 1.2 m and then carries the block horizontally a distance of 7.3 m. Determine the work done by the person and by the force of gravity in this process. 8. A plane designed for vertical takeoff has a mass of 8.0 × 103 kg. Find the net work done by all forces on the plane as it accelerates upward at 1.0 m/s2 through a distance of 30.0 m after starting from rest. 4. When catching a baseball, a catcher’s glove moves by 10 cm along the line of motion of the ball. If the baseball exerts a force of 475 N on the glove, how much work is done by the ball? 5. A flight attendant pulls her 70.0 N flight bag a distance of 253 m along a level airport floor at a constant velocity. The force she exerts is 40.0 N at an angle of 52.0° above the horizontal. Find the following: a. the work she does on the flight bag b. the work done by the force of friction on the flight bag c. the coefficient of kinetic friction between the flight bag and the floor Section2 Energy Summery : • Objects in motion have kinetic energy because of their mass and speed. • The net work done on or by an object is equal to the change in the kinetic energy of the object. • Potential energy is energy associated with an object’s position. Two forms of potential energy discussed in this chapter are gravitational potential energy and elastic potential energy. Revision questions : 1. A 6.0 kg cat runs after a mouse at 10.0 m/s. What is the cat’s kinetic energy? 2. When a 2.00 kg mass is attached to a vertical spring, the spring is stretched 10.0 cm such that the mass is 50.0 cm above the table. a. What is the gravitational potential energy associated with this mass relative to the table? b. What is the spring’s elastic potential energy if the spring constant is 400.0 N/m? c. What is the total potential energy of this system? 3. A person drops a ball from the top of a building while another person on the ground observes the ball’s motion. Each observer chooses his or her own location as the level for zero potential energy. Will they calculate the same values for: a. the potential energy associated with the ball? b. the change in potential energy associated with the ball? c. the ball’s kinetic energy? 4. Can the kinetic energy of an object be negative? Explain your answer. 5. Can the gravitational potential energy associated with an object be negative? Explain your answer. 6. 14. Two identical objects move with speeds of 5.0 m/s and 25.0 m/s. What is the ratio of their kinetic energies? 7. 19. What is the kinetic energy of an automobile with a mass of 1250 kg traveling at a speed of 11 m/s? 8. What speed would a fly with a mass of 0.55 g need in order to have the same kinetic energy as the automobile in item 19? 9. A 50.0 kg diver steps off a diving board and drops straight down into the water. The water provides an upward average net force of 1500 N. If the diver comes to rest 5.0 m below the water’s surface, what is the total distance between the diving board and the diver’s stopping point underwater? Section3 conservation of energy Summery : • Energy can change form but can never be created or destroyed. • Mechanical energy is the total kinetic and potential energy present in a given situation. • In the absence of friction, mechanical energy is conserved, so the amount of mechanical energy remains constant. Revision questions: 1. A small 10.0 g ball is held to a slingshot that is stretched 6.0 cm. The spring constant is 2.0 × 102 N/m. a. What is the elastic potential energy of the slingshot before it is released? b. What is the kinetic energy of the ball just after the slingshot is released? c. What is the ball’s speed at that instant? d. How high does the ball rise if it is shot directly upward? 2. Each of the following objects possesses energy. Which forms of energy are mechanical, which are nonmechanical, and which are a combination? a. glowing embers in a campfire b. a strong wind c. a swinging pendulum d. a person sitting on a mattress e. a rocket being launched into space 3. Discuss the work done and change in mechanical energy as an athlete does the following: a. lifts a weight b. holds the weight up in a fixed position c. lowers the weight slowly 4. A ball is thrown straight up. At what position is its kinetic energy at its maximum? At what position is gravitational potential energy at its maximum? 5. A child and sled with a combined mass of 50.0 kg slide down a frictionless hill that is 7.34 m high. If the sled starts from rest, what is its speed at the bottom of the hill? 6. Tarzan swings on a 30.0 m long vine initially inclined at an angle of 37.0° with the vertical. What is his speed at the bottom of the swing if he does the following? a. starts from rest b. starts with an initial speed of 4.00 m/s Section4 power Summery: • Power is the rate at which work is done or the rate of energy transfer. • Machines with different power ratings do the same amount of work indifferent time intervals. Revision questions : 1. Two horses pull a cart. Each exerts a force of 250.0 N at a speed of 2.0 m/s for 10.0 min. a. Calculate the power delivered by the horses. b. How much work is done by the two horses? 2. If an automobile engine delivers 50.0 hp of power, how much time will it take for the engine to do 6.40 × 105 J of work? (Hint: Note that one horsepower, 1 hp, is equal to 746 watts.) 3. Water flows over a section of Niagara Falls at the rate of 1.2 × 106 kg/s and falls 50.0 m. How much power is generated by the falling water? 4. Which of the following equations correctly describes the relation between power, work, and time?
