PHYS 2111 - Expt 6 Work and Energy

Inclined Plane: Work & Energy Objective The objectives of this lab are:  To understand the concept of work, energy and power,  To be able to distinguish between potential energy and kinetic energy,  To develop and understanding of how work can be measured,  To understand the concept of mechanical energy of a system and energy conservations, Introduction This lab is about examining the concepts of work, energy and power. We will explore some of the systems we have used in other experiments this semester. We hear these words (work, energy and power) several times in a day without giving them much thought, but today you will have the opportunity to quantify them. You will begin by comparing your intuitive, everyday understanding of work, energy and power with their formal mathematical definition. You will first consider the work done on a small object by a constant force. However, there are many cases where the force is not constant. For example, the force exerted on a spring increases the mass hanging on it. In this lab you will explore how to measure and calculate the work done by any force that acts on an object. It is often useful to know the total amount of work that is being done, and also the rate at which it is done. The rate at which work is done is referred to as power . Energy (and the concept of conservation of energy) is a powerful and useful concept in all the sciences. It is one of the more challenging concepts to understand. You will begin the study of energy in this lab by considering kinetic energy – a type of energy which depends on the change in the velocity of an object and its mass. If we compare the change of an objects kinetic energy to the net work done on it, it is helps us investigate the concept of the Work — Energy Principle . You will study a Dynamic Cart being pulled up an inclined plane (θ ranging from 0 – 45 o ) by a force applied through a spring. How much work is done on the cart when it from point A to point B ? What is the kinetic energy change of the cart? How is the change in kinetic energy related to the net work done on the cart by the spring? These are questions you will investigate throughout this lab. When we lift a load/object against the earth’s gravitational pull, work is done. The more the mass of the object or the higher it is lifted, the more the work that is done is doing the activity. The same concept is applied for dragging or pushing something across the floor. Therefore, the term work is defined as the product of force and displacement, it is mathematically defined as; 𝑊 = ?. ? = ????𝑠𝜃 (1) Where W is work, F is the force applied, d is the displacement and θ is the angle between the force and the displacement.

It is essential to note that energy is one of the most important concepts in science and our universe is made of matter and energy. The concept of matter is easy to comprehend because it can be seen, felt, smelled, etc., basically we can interact with it. Energy on the other hand cannot be experienced in that way – however, it can be measured based on its interactions with matter. Energy has metric unit of Joules (J) 1 Joule is the amount of energy needed to move a weight/force of 1 Newton through a distance of 1 meter. Therefore, the fundamental unit of a Joule is a Nm. The English System’s unit of energy is a calorie (cal) – 1 cal is the energy required to raise the temperature of 1g of water by 1 o C. Another very common unit of energy related to calories is the kilocalorie (kcal). A kilocalorie is 1000 little calories. The relationship between Joules and Calories is 4184 J = 1 kcal which means that 4.184 J = 1 cal. Work can be done at various rates just as energy can be changed at various rates. The rate of change of work is a measure of power. Mathematically power is defined by the relation: 𝑃 = 𝑊 ? (2) Where P is the power, W the work done and t is the time taken. The unit of power is Watts which is equivalent to a Joule per second (Js -1 ). It is also interesting to note that in an attempt to slide (or attempts to slide) an object over a surface, there is generally some force that opposes the sliding motion which is termed friction . There are generally two kinds of friction, in terms of their effects: static friction , which keeps two surfaces “stuck together” (stationary with respect to each other), and kinetic friction , which opposes an ongoing sliding motion. In this experiment we will study both static and kinetic frictional forces. The kinetic frictional force is generally less than the maximum value of the static frictional force for a given material. In general, a static frictional force is related to the normal force and its maximum value is given by the relation: 𝑓 ? 𝑚𝑎𝑥 = 𝜇 ? ? 𝑁 (3) Similarly, the kinetic frictional force is given by the relation: 𝑓 𝑘 = 𝜇 𝑘 ? 𝑁 (4) Where 𝜇 ? the Coefficient of Static Friction, 𝜇 𝑘 is the Coefficient of Kinetic Friction and N is the Normal Force.

Activity I: Work and Change in Gravitational Potential Energy 6. At the bottom of the screen should have a “ small crate ” . The mass, the coefficient of kinetic friction and the coefficient of static friction are all given. 7. Use equation 3 to calculate the maximum static frictional force that must be overcome before the crate can move. Show your calculations 8. With the answer from step 7 in mind, enter a value in the box next to the applied force and click on the play button so that with that applied force, the crate can be pushed to the about the 6.0 m mark on the inclined plane. Note: To change the value of the applied force. Click on the “ Reset All ” at the bottom of the menu to the right of the screen, then enter the new number and click on play. 9. Take a screenshot for your report. 10. Record the applied force, the angle of the inclined, the coefficient of kinetic friction, how far the crate has moved (part on the flat surface and part on the inclined surface) 11. With the values in step 10, calculate the net work done in pushing the crate from the -6.0 m mark to the new mark on the inclined surface. 12. Calculate the work done by the gravitational force ? 𝑔 13. Using the potential energy relation (PE = mgh), calculate the change in potential energy between the starting point of the crate and where it stopped on the incline plane. Note that you can use trigonometry relations to find the height of the crate from the horizontal surface. 14. How does your results in step 11 and step 13 compare? Explain. 15. What is the direction of the frictional force at the stopping point on the inclined? 16. How does the angle affect the direction of the frictional force

Activity II: Work done and Kinetic Energy In this part of the experiment we would use the work energy theorem. Note that all the forces present are not conservative. We know: 𝑊 = ∆𝐾? 𝑎?? 𝑊 = −∆𝑃? 1. Click on “ Reset All ” at the bottom of the right menu 2. On the menu on the right side of the screen, change the object position under “ more controls ” to 8 and press the Enter button on your keyboard. 3. Record the position where the crate stops. 4. Repeat step 2 for 6, 4 and 2 m and for each position record where the crate stops on the horizontal surface 5. Could you use this information to verify the mass of the crate? Show your work. Activity III: Unknown Mass Click on the “ Reset All ” at the bottom of the right menu 1. Select the Mystery object from the drop down menu ay clicking in the icon and select the mystery object from the drop down list. 2. Repeat steps 2, 3 and 4 from activity II 3. Find the mass of the Mystery object