Download Lab 2 – Newton`s Laws of Motion INTRODUCTION

North Carolina State University PY131 Lab Manual Lab 2 – Newton’s Laws of Motion Lab 2 – Newton’s Laws of Motion INTRODUCTION Gravitational force keeps you on the ground, causes objects to fall toward the Earth, and keeps the moon in orbit. Gravitational force is an attractive force between two masses (you and the Earth, for example). Thus, while the Earth exerts a downward force on you, you in turn exert an upward force on the Earth! In fact, everything with mass in the universe exerts an attractive force (pulling force) on everything else with mass in the universe. Isaac Newton realized that the gravitational attraction between two objects is proportional to the masses of those objects and inversely proportional to the square of the distance between the two objects. This is mathematically expressed as F =G
m1 m 2
r2
where m1 and m2 are the masses of the two objects, r is the distance between the two objects and G is a constant known as the gravitational constant. €
From the above equation, you can see that, if you double the mass of either one of the objects, the attractive force would also double. If you move the two objects twice as far apart (double the distance between them), the force of gravity would decrease by a factor of four. The gravitational force exerted by the earth on objects near or on its surface reduces to F = mg where g is the gravitational acceleration due to the earth’s gravitational force. All objects, regardless of their mass, will fall down toward the surface of the earth with acceleration g. If m is in kg and g is €
in m/s2, then the force will be in Newtons. If you drop a sheet of paper and a penny, the penny will hit the ground first. This might lead you to conclude that gravity accelerates a penny faster than a sheet of paper. But gravity isn't the only force acting on the penny and the sheet of paper. Air resistance opposes (with different effects) the downward motion of the paper and penny. If you were able to repeat this experiment inside a vacuum chamber, where the only force involved is gravity, the penny and the sheet of paper would hit the ground at exactly the same time. Now you might correctly conclude that all objects are accelerated by gravity at the same rate regardless of their shape or mass. This has been the accepted theory since Galileo and later Newton expressed it in the 17th Century. 1 North Carolina State University PY131 Lab Manual Lab 2 – Newton’s Laws of Motion Force and Acceleration Newton’s Second Law is defined as “the acceleration of an object is directly proportional to the net force acting on the object, is in the direction of the net force, and is inversely proportional to the mass of the object.” Mathematically this can be written as F = ma When a force F acts on an object of mass m, it has an acceleration. If m is measured in kg and a is in m/s2, the force will be in units of Newton (usually represented by ‘N’). The mass m of an object is the quantity of matter in that object. Your mass is the same whether you are on the moon, on Earth, on Jupiter, or in deep outer space. The weight of any object is the gravitational force acting on the object. The acceleration due to gravity is different on the surface of the moon, Earth, Jupiter etcetera. Therefore, while your mass remains constant your weight varies. The acceleration due to gravity close to the surface of the Earth is g = 9.8 m/s2 = 32 ft/s2. Newton’s Third Law states that “whenever one object exerts a force on a second object, the second object exerts an equal and opposite force on the first”. Consider the fact that you are not plunging toward the center of the earth while sitting on your lab chair. There are two equal but opposite forces acting on you in this situation. The Earth exerts a downward force on you and this is your weight pressing down on the seat. The chair seat exerts an equal but opposite upward force on you. As a result, the net force on you is zero. Another way to state Newton’s Third Law is “for every action there is an equal and opposite reaction”. In this lab, you will conduct two experiments: The first to investigate the relationship between force and acceleration, the second to investigate the effects of gravity on falling objects. PROCEDURE Part A: Investigating Forces In this part of the Lab, you will use a bathroom scale to investigate the forces acting on a person while in the classroom. You will make observations on the scale’s reading and draw some force diagrams. Note: You will be measuring the force in units of lbs rather than in units of Newton. 1. Place the scale on the surface of the lab table. With your arms straight and elbows locked, place your hands on the scale while leaning over the scale and with your feet slightly back. Observe the weight. 2. It should read between 40 and 50 lbs. Record this constant weight and draw a force diagram for this on the worksheet. 2 North Carolina State University PY131 Lab Manual Lab 2 – Newton’s Laws of Motion 3. Keep your hands on the scale and now bend your elbows allowing it to fall toward the scale. What happens to the weight? Why? Record the weight and draw a force diagram to describe the situation. 4. Keep your hands on the scale and in a modified push-­‐up lower your upper body towards the scale and move your hips toward the lab bench. What happens to the weight? Why? Record the weight and draw a force diagram to describe the situation. CHECKPOINT 1: HAVE YOUR TA CHECK YOUR WORK BEFORE PROCEEDING Part B: Elevator Ride In this part of the Lab, you will use a bathroom scale to investigate the forces acting on a person riding in an elevator. You will collect data on how the scale’s reading changes during the elevator ride. Because the scale reading will be in lbs (and not Newtons), you will have to use g = 32 ft/s2. 5. Have one group member stand on a bathroom scale inside an elevator on the ground floor. 6. Ride the elevator from the bottom floor to the top floor and back. At each of the elevator positions identified in the figure on the worksheet, record the scale’s reading and draw a force diagram showing all significant forces acting on the person. 7. Repeat step 6 one more time and take the average of the two values of the scale. If the elevator accidentally stops at any floor along the way, void that data and start again. 8. Complete the "Net Force" and "Acceleration" columns in the data table on the worksheet. As you do this, recall the relationship between force and acceleration that is given by Newton's Second Law. CHECKPOINT 2: HAVE YOUR TA CHECK YOUR WORK BEFORE PROCEEDING Part C: Falling Objects SAFETY FIRST! Select a location at least three stories high that is safe and secure where no one below could be hit when objects are dropped. 3 North Carolina State University PY131 Lab Manual Lab 2 – Newton’s Laws of Motion 9. You have available to you, several objects of varying shapes, sizes and masses that you can drop from a balcony of your lab building. 10. Estimate the distance of fall for the objects and record this on the worksheet. 11. Drop the objects one at a time, measure the time taken for each one to reach the ground and record the value in the data table on the worksheet. 12. Repeat step 11 twice for each object and find the average time of drop for each object. 13. Calculate the acceleration of each object using the equation a =
2h
. t2
CHECKPOINT 3: HAVE YOUR TA CHECK YOUR WORK BEFORE PROCEEDING €
4 North Carolina State University PY131 Lab Manual Lab 2 – Newton’s Laws of Motion NEWTON’S LAWS OF MOTION – Worksheet Part A: Investigating Forces FORCE DIAGRAM (A) FORCE DIAGRAM (B) Scale Reading = _____________lbs CHECKPOINT 1 Scale Reading = _____________lbs FORCE DIAGRAM (C) Scale Reading = _____________lbs Part B: Elevator Ride GOING UP Ground Floor First Floor FORCE DIAGRAM 5 Second Floor Third Floor North Carolina State University PY131 Lab Manual Lab 2 – Newton’s Laws of Motion COMING DOWN Third Floor Second Floor First Floor Ground Floor FORCE DIAGRAM Weight of rider = ___________ lbs Position Average Scale Reading (lbs) Ground floor at rest Net Force on Person (lbs)  Acceleration of Person (ft/s2)  Starting up, just above ground floor Midway Heading up Slowing down, approaching top floor Top floor at rest Starting down, just below top floor Midway Heading down Slowing down, approaching ground floor  All upward forces and acceleration are positive and all downward forces and acceleration are negative. In which direction and with what acceleration should the elevator move in order for you to experience weightlessness? 6 North Carolina State University PY131 Lab Manual Lab 2 – Newton’s Laws of Motion CHECKPOINT 2 Part C: Falling Objects Estimated distance of fall = _____________ m
Time (s) Acceleration (m/s2) Object Time 1 Time 2 Average 1. Did all the objects fall down with the same acceleration? 2. If they did not, what might be the reason(s) for the different values you got for the acceleration? CHECKPOINT 3: 7