E104 Newton's Second Law of Motion

Graphs Part A. Constant Mass, Changing Net Force

Acceleration vs. Net Force 3

2.5

0.98, 2.5025

Acceleration(m/s2)

0.784, 2.17 2 0.588, 1.6656

1.5 Acceleration vs Net Force

0.392, 1.087

1

0.196, 0.5601

0.5

0 0

0.2

0.4

0.6

0.8

1

1.2

Net Force (N)

Interpretation: The relationship between the acceleration to net force is that, as the acceleration increases, the net force also increases, and vice versa. The slope of the graph is , where is constant. Integrating, the graph is a curve with inverse logarithmic equation. It has no intercepts because there is no trial conducted that includes no mass (weight) at all, regardless if it is the mass from the hanging object. Hence, it is apparent that acceleration is directly proportional to the net force if the mass of the body is constant.

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Part B. Changing Mass, Constant Net Force

Acceleration vs Mass 3 0.51924, 2.6116

2.5

Acceleration(m/s2)

0.61924, 2.2874 2

0.71924, 1.9099 0.81924, 1.7688 0.91924, 1.5938

1.5

Acceleration vs Mass 1

0.5

0 0

0.2

0.4

0.6

0.8

1

Mass(kg)

Interpretation: In acceleration vs. mass, it is shown that as the mass increases, the acceleration decreases. Conversely, as the acceleration increases, the mass decreases. Its slope is negative. This graph has an inverse power equation. This follows that when the cart is loaded (increase in mass, a resisting force), the acceleration decreases. Thus it can be inferred that acceleration is inversely proportional to mass when the net force of the body is kept constant.

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Problem 1. If the mass of the cart in the experiment is 520g and the total hanging mass is 200 g, how long will the cart travel a distance of 100 cm starting from rest? Given:

Required: Solution: i.)

ii.)

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Interpretation of Results Newton’s second law of motion states that if a net external force acts on a body, the body accelerates. The direction is the same as the direction of the net force. The mass of the body times the acceleration of the body equals the net force vector. Force can also be described by intuitive concepts such as a push or pull that can cause an object with mass to change its velocity (which includes beginning moving from a state of rest). A force can be expressed in terms of Newton (1 N = 1 kg m/s2). The gravity of the earth causes the pulling force on any object (mass) near its surface. This force is the acceleration measured in metes per second per second (in symbols, m/s2 or m·s-2) or in Newtons per kilogram (N/kg or N·kg-1). It has an approximate value of 9.81 m/s2, which means that, ignoring air resistance, the speed of an object falling freely near the Earth's surface increases by about 9.81 meters per second every second. Mass is often used interchangeably with weight, and the units of weight are often taken to be kilograms (for instance, a person may state that his weight is 75 kg). In proper scientific use, however, the two terms refer to different, yet related, properties of matter. Mass is different from weight, mass (inertial) of an object measured by its resistance to acceleration, while weight is the name given to the force on an object due to gravity. For instance, an object with a mass of one kilogram will have a weight of 9.8N on the surface of the Earth. Mass could exist without gravity. Thus, in outer space, one would be weightless, but not mass-less. Net force is the overall force acting on an object when all the individual forces acting on the object are added together. This must be applied to a mass (object) to produce acceleration. Acceleration f a body is in the same direction as the net force acting on the body, and is equal to the net force divided by the body’s mass. Newton’s second law is a fundamental law of nature, the basic relationship between force and motion. In this experiment we use a dynamics cart with weight hanger attached connected by strings supported by dynamics cart with pulley. There are two photogates which will detect the movement of the cart with picket fence, and the smart timer which will measure the time travelled. By varying the mass of the weight and the cart, measurements can be taken verifying Newton's 2nd Law. Note that the dynamics track is frictionless and the environment is suitable for not having air resistance, thus, not a valid reason for getting erroneous results, such that the velocity of the glider remains essentially constant. In Part 1 (constant mass, changing net force) of the experiment, the net force (m2g, where m2 is the total hanging mass and g is gravitational pull=9.81 m/s2) varies when the weight of the hanging object connected to the cart change, thus getting different accelerations. The force’s direction is downward. constant is the mass of the hanging object while the cart’s mass is constant. Tension is the magnitude of the pulling force exerted by a string (used in the experiment), cable, chain, or similar object on another object; is to be considered either acceleration is zero and the system is therefore in equilibrium, or there is acceleration and therefore a net force is present. Note that a string is assumed to have negligible mass. The cart’s fixed mass is 0.5067 kg; we consider the mass (m1) to be the mass of the cart + mass of the picket fence (which is 0.01254 kg) with a total of 0.51924 kg. Increasing the weight .20kg per trial, we get an increasing acceleration. The experiment’s resulting data shows that, as we increase the mass of the pulling object, its net force do the same way too, so thus the acceleration. In Part A. of the graphs, the relationship between the acceleration to net force is that, as the acceleration increases, the net force also increases, and vice versa. Hence, we can say that the acceleration is directly proportional to the net force as to the mass of the object (when it is constant). In Part 2 (changing mass, constant net force) which the mass of the cart is changing and the hanging object is the constant. The mass of the cart is added a mass of 0.100 kg per trial. As we can observe, while we pile up the College Physics Part 1

weights to the cart, the acceleration drops from 2.6116 m/s2 to 1.5938 m/s2. Greater load on the cart is equal to greater resistance against movements. This is associated by the pulling gravity upon the cart. In Part B. of the graphs, the acceleration vs. mass, it is shown that as the mass increases, the acceleration decreases. Conversely, as the acceleration increases, the mass decreases. Thus it can be inferred that acceleration is inversely proportional to mass when the net force of the body is kept constant. In Part 3 (changing mass, changing net force) mass of cart and the net force are both changing variables. Here, we add the mass of the cart, 0.100 kg on 2nd trial, 0.200 kg, 0.300 kg and 0.400 kg on succeeding trials. While the hanging object increase from 0.020 kg (on first trial) to 0.040 kg, 0.060 kg, 0.080 kg and 0.100 kg on next turns. Although greater mass was added to cart, net force still overcomes its resisting force. Thus, the acceleration is increasing. . It is true using the equation , where m2 is the mass of the hanging mass showing direct proportionality of it with acceleration. Percent errors we obtained are not higher than 40% but not even lower than 35%. Such large errors are neither to be blame on the smart timer, friction nor air resistance. Those are obtained from discrepancies on the placement of photogates (20 cm and 70 cm), the starting (releasing) point of the dynamics cart (which is placed on 0 cm part of the dynamics track) and the table where we place the experiment’s equipment. Let’s discuss first the table where the dynamics track is at. When we first place the dynamics cart on the dynamics track, we observe that when we made it at rest, it suddenly moves to the beginning of the track (to 0 cm). We think that the table is not that well flattened. Though I think it contributes a very little error. Next is the photogates. When we launched the dynamics track each trial, I see that the track moves forward because of the push or impact of the cart to the track’s end. Hence, the track moves while the photogates are at rest, thus keeping us to place the photogates in its proper position. But sometimes we forget to do it. Though, it doesn’t contribute that much error. Lastly, the greatest contributor of error is the releasing point of the cart. As I realized, when we release the cart at 0 cm (at the back end of the cart) as shown in Fig. 1, the velocity instead of a 0 value, it has greatly than 0. The right way to correct it is shown in Fig. 2, we should place the cart with the picket fence exactly at 20 cm where the first photogate is located, where the photogate will blink the instant the cart moves, so that the velocity will be 0. And we know that acceleration describes how the velocity changes with respect to time: . Doing this will surely greatly decrease the percent error from 40% to possibly less than 4%.

| Fig. 1

Fig.2

Credits to: DANNA MAY MENDEZ VON_SCIENCEO8 En.Wikipedia.org http://www.physicsclassroom.com http://hyperphysics.phy-astr.gsu.edu other credits that are not mention, credits to you. College Physics Part 1