LAB_REPORT_2-1PH3 (1)

MCMASTER – MOHAWK JOINT VENTURE BACHELOR OF TECHNOLOGY PARTNERSHIP FOUR-YEAR UNIVERSITY DEGREE PROGRAMS EXPERIMENT NO: TITLE: Submitted by: Lab Section: Partner: Instructor: Date lab performed: Date of submission: EXPERIMENT NO. 2 FORCE AND ACCELERATION ENG TECH 1PH3 Page 1

PURPOSE: To study the acceleration of a free falling body to determine g, the acceleration due to gravity, and to study the effect of changing the mass and the force on acceleration. APPARATUS: Lab cart (Hall's carriage), Spark timing device, Power supply, Spark sensitive paper, Tape, Meter stick, Weights, Clamps, Thread, Pulleys, Retort stand, Spring balance, Balance. THEORY: An object falling in a gravitational field picks up speed as it falls. This implies that its velocity changes (in this case, increases) with time. The rate of change of velocity with time is called acceleration. This may be written as: Δ v v − v a = = 0 t t where: a = acceleration (m/s 2 ) v = final velocity (m/s) v 0 = initial velocity (m/s) t = time (s) For a period of constant acceleration the displacement, x, of a moving object (distance object travels) is the average velocity times the time period for the motion. The average velocity is the sum of starting velocity plus final velocity all divided by 2. ⎛ v + v 0 ⎞ x = v × = t ⎜ ⎟ × t ⎝ 2 ⎠ From equation (1) it is possible to manipulate the equation to solve for v. v = a × t + v 0 (1) If we substitute this value for v into the equation that defines x, the displacement can be expressed as: ⎛ v + v 0 ⎞ x = ⎜ ⎟ × t ⎝ 2 ⎠ ⎛ a × t + v 0 + v 0 ⎞ x =⎜ ⎟× t ⎝ 2 ⎠ ⎛ a × t + 2 v 0 ⎞ x =⎜ ⎟× t ⎝ 2 ⎠ a × t 2 + 2 v 0 × t x = 2 ENG TECH 1PH3 Page 2

x = a × t 2 + v 0 × t x = at 2 + v 0 t x α t 2 (2) The displacement is proportional to t 2 , when v 0 is zero. The acceleration of a free falling object is commonly referred to as the acceleration due to gravity, g. This value is approximately constant for the earth and is 9.81 m/sec 2 . This acceleration is a constant value because it depends on the mass and radius of the earth and does not depend on the mass of the object. A force may be defined as a push or pull that changes or tends to change the motion of an object. A change in motion is another term for acceleration. Newton's 2 nd law describes the relationship between force, mass and acceleration. It is a general description of the effect an unbalanced force will have on an object, and may be written as: force = mass × acceleration or, more simply: f = m × a = ma where: f = force acting on an object causing it to accelerate (Newtons, N) m = mass of the object undergoing acceleration (kilograms, kg) a = acceleration of the object (m/s 2 ) Newton's law of universal gravitation describes a particular force that exists because of mass. It is an attractive force that pulls together two objects of masses M 1 and M 2 . This attraction decreases with the square of the distance between the masses. The universal gravitational constant, G, compensates for our earth-based metric system. The force of gravity, f g is defined by: G × M 1 × M 2 GM 1 M 2 f g = 2 = 2 r r where: f g = gravitational force (N) M 1 = mass of first object (kg) M 2 = mass of second object (kg) r = distance between objects (m) G = universal gravitational constant = 6.67×10 -11 (N-m 2 /kg 2 ) Now if we consider the gravity between the earth (mass M e ) and an object of mass m that is close to the surface of the earth, the distance between the object and the centre of the earth is essentially the radius of the earth, r e . The force of gravity, f g , is: G × M e × m GM 1 M 2 f g = 2 = 2 r e r But force is also defined by: f = m × a ENG TECH 1PH3 Page 3

Since f must equal f g , we can equate the equations to get: Dividing by m we get G × M × m m × a = 2 e r e G × M a = 2 e r e G, M e , the mass of the earth and r e , the mean radius of the earth, are all constant. The acceleration caused by gravity (close to the surface of the earth) is also constant and is equal to 9.81 m/s 2 . If objects of different masses fall at different rates, such as a nail and a feather, it is because the force of air friction acting on the feather is greater than the air friction acting on the nail. In a vacuum, the feather and the nail fall at the same rate (see Figure 2.1). In this experiment, the student will determine the acceleration of gravity at the surface of the earth, g, and measure changes in acceleration as mass and the accelerating force are changed. In order to measure acceleration the student will use a timing device that marks a moving paper tape at regular time intervals (see Figure 2.2 ). The distance between the marks should be increasing if the object is undergoing acceleration because although the time difference between when the dots are made is the same, the actual distance between the dots is increasing with time as the tape is be speeding up. In this particular case, the time between dots is l/60 th of a second. Figure 2.1 Figure 2.2 1 By measuring the distance from the first dot to consecutive dots we can calculate the velocity at every newl/60 th of a second interval. Knowing the change in velocity from a period of l/60 th of a second to the next allows the student to calculate the acceleration due to gravity. Figure 2.3 shows the paper tape connected to a thread which is run through a series of pulleys in order to allow the mass to fall from a greater height and permit sufficient points on the tape to make the 1 Nakamura Spark Timer, Sargent-Welch, www.sargentwelch.ca. ENG TECH 1PH3 Page 4