Chapter 4: Forces and Newton's laws of motion

Free body diagrams

1. Identify all the forces acting on the object 2. Draw a coordinate system 3. Represent the object as a dot at the origin of the coordinate axes 4. Draw vectors representing each of the identified forces 5. Draw and label the net force vector

Newton's second law

A force causes an object to accelerate. The acceleration (a) is directly proportional to the force F and inversely proportional to the mass M a = F/M Or F = Ma Note that if we double the size of the force F, the acceleration a will double, as we found experimentally. And if we triple the mass m, the acceleration will be only 1/3 as great.

What is a force?

A force is a push or a pull. A force acts on an object and requires an agent. A force is also a vector. It can also be either a contact force or a long range force.

You've just kicked a rock, and it is now sliding across the ground about 2 meters in front of you. Which of these are forces acting on the rock? List all that apply. A. Gravity, acting downward B. The normal force, acting upward C. The force of the kick, acting in the direction of motion D. Friction, acting opposite the direction of motion E. Air resistance, acting opposite the direction of motion

A, B, and D. Friction and the normal force are the only contact forces. Nothing is touching the rock to provide a "force of the kick." You can ignore air resistance unless the problem specifically calls for it.

|| Two children fight over a 200 g stuffed bear. The 25 kg boy pulls to the right with a 15 N force and the 20 kg girl pulls to the left with a 17 N force. Ignore all other forces on the bear (such as its weight). At this instant, can you say what the velocity of the bear is? If so, what are the magnitude and direction of the velocity? At this instant, can you say what the acceleration of the bear is? If so, what are the magnitude and direction of the acceleration?

A.No b. 10 m/s2 to the left

Newton's first law

An object has no forces acting on it. If it is at rest, it will remain at rest. If it is moving, it will continue to move in a straight line at a constant speed.

A constant force is applied to an object, causing the object to accelerate at 8.0 m/s2. What will the acceleration be if The force is doubled? The object's mass is doubled? The force and the object's mass are both doubled? The force is doubled and the object's mass is halved?

Answer : a. 16 m/s2 b. 4.0 m/s2 c. 8.0 m/s2 d. 32 m/s2

Two rubber bands stretched to the standard length cause an object to accelerate at 2 m/s2. Suppose another object with twice the mass is pulled by four rubber bands stretched to the standard length. What is the acceleration of this second object? 1 m/s2 2 m/s2 4 m/s2 8 m/s2 16 m/s2

Answer: 2 m/s^2 because Acceleration is proportional to force, so doubling the number of rubber bands doubles the acceleration of the original object from 2 m/s2 to 4 m/s2. But acceleration is also inversely proportional to mass. Doubling the mass cuts the acceleration in half, back to 2 m/s2.

The motion of a very massive object can be minimally affected by what would seem to be a substantial force. Consider an oil supertanker with mass 3.0*10^8 kg. Suppose you strapped two jet engines (thrust) onto the sides of the tanker. Ignoring the drag of the water (which, in reality, is not a very good approximation), how long will it take the tanker, starting from rest, to reach a typical cruising speed of 6.0 m/s?

Answer: 5 hours

A car has a maximum acceleration of 10.0 m/s2. What will the maximum acceleration be if the car is towing another car of the same mass?

Answer: 5 m/s2

A boy is using a rope to pull a sled to the right. What are the directions of the tension force and the friction force on the sled, respectively? A. Right, right B. Right, left C. Left, right D. Left, left

Answer: B.

A block has acceleration a when pulled by a string. If two identical blocks are glued together and pulled with twice the original force, their acceleration will be A. (1/4)a B. (1/2)a C. a D. 2a E. 4a

Answer: C

Electric and Magnetic forces.

Electricity and magnetism, like gravity, exert long-range forces. The forces of electricity and magnetism act on charged particles. (Don't really need to know this).

Drag

Friction at a surface is one example of a resistive force, a force that opposes or resists motion. This kind of resistive force—the force of a fluid on a moving object—is called drag and is symbolized as D. Like kinetic friction, drag points opposite the direction of motion.

Net force

It is the vector sum of all the forces. F1 +F2+F3 ... = Fnet

Spring force

Springs exert one of the most basic contact forces. A spring can either push (when compressed) or pull (when stretched). The symbol for Spring Force is Fsp.

Weight

The gravitational pull of the earth on an object on or near the surface of the earth. The symbol for weight is w. An object's weight vector always points vertically downward, no matter how the object is moving.

Thrust

Thrust occurs when a jet or rocket engine expels gas molecules at high speed. Thrust is a contact force, with the exhaust gas being the agent that pushes on the engine. Thrust is a force opposite the direction in which the exhaust gas is expelled. There's no special symbol for thrust, so we will call it Fthrust.

A baseball player is sliding into second base. Identify the forces on the baseball player.

Weight, normal force by ground, kinetic friction force by ground

A skier is sliding down a 15° slope. Friction is not negligible. Identify the forces on the skier.

Weight, normal force by slope, kinetic friction force by slope

A mountain climber is hanging from a vertical rope, far above the ground and far from the rock face. Identify the forces on the mountain climber.

Weight, tension force by rope

Tension force

When a string or rope or wire pulls on an object, it exerts a contact force that we call the tension force, represented by T. The direction of the tension force is always in the direction of the string or rope.

Normal force

the force exerted by a surface (the agent) against an object that is pressing against the surface. The symbol for the normal force is n. The normal force is perpendicular to the surface.

Force vectors

1. Represent the object as a particle. 2. Place the tail of the force vector on particle. 3. Draw it pointing in the direction that the forces acts with a length proportional to the size of the force 4. Give the vector an appropriate label

What are the eight forces?

1. Weight 2. Spring force 3. Tension force 4. Normal Force 5. Friction 6. Drag 7. Thrust 8. Electric and magnetic forces

Newton's third law

Every force occurs as one member of an action/reaction pair of forces. The two members of an action/reaction pair act on two different objects. The two members of an action/reaction pair point in opposite directions and are equal in magnitude.

Scallops use jet propulsion to move from one place to another. Their shells make them denser than water, so they normally rest on the ocean floor. If a scallop wishes to remain stationary, hovering a fixed distance above the ocean floor, it must eject water so that the thrust force on the scallop is . A. upward, upward B. upward, downward C. downward, upward D. downward, downward

Answer: C.

Tennis balls experience a large drag force. A tennis ball is hit so that it goes straight up and then comes back down. The direction of the drag force is Always up. Up and then down. Always down. Down and then up.

Answer: Down and then up

A beach ball is thrown straight up, and some time later it lands on the sand. Is the magnitude of the net force on the ball greatest when it is going up or when it is on the way down? Or is it the same in both cases? Explain. Air resistance should not be neglected for a large, light object.

Answer: Greater on the way up

A car has a maximum acceleration of 8.4 m/s2 . What will the maximum acceleration be if the car is towing another car of the same mass? Neglect the additional friction force.

Answer: a= 4.2 m/s^2

A falcon is hovering above the ground, then suddenly pulls in its wings and begins to fall toward the ground. Air resistance is not negligible. Indentify the forces on the bird.

Answer: drag and weight.

Friction

Friction, like the normal force, is exerted by a surface. Unlike the normal force, however, the frictional force is always parallel to the surface, not perpendicular to it. (In many cases, a surface will exert both a normal and a frictional force.) The symbol for friction is f. 1. Kinetic friction, denoted by fk, acts as an object slides across a surface, it is always "opposed the motion". 2. Static friction, denoted by fs, is the force that keeps an object "stuck" on a surface and prevents its motion relative to the surface. It points in the direction necessary to prevent motion.