Question 1 Draw a free body diagram of the block and cart (treated as a single mass) as soon as they leave the spring at the top of the ramp. Free body diagram 0.5 0MTlA - Forces in Motion Rationale As engineers, it is important to understand how energy can be converted from one form to another and how losses affect the efficiencies of systems. In this experiment, you will investigate the effect of friction on a system and thereby gain an understanding of how thermal losses affect the efficiencies of mechanical systems. Objective To determine the thermal energy generated by a block sliding down a slope. Theory Mechanical energy is the sum ofthe potential energy (elastic and gravitational) and kinetic energy ofa system. When a system is subjected to conservative forces such as gravity (assuming no air resistance) or an undamped spring, energy is conserved and converted from one form of mechanical energy to another. However, when a non-conservative force (e.g., friction) acts on the system, energy is irretrievably lost from the system. This can be expressed as: Kinitial + Uinitial + Won system : Knal + Uflnal + Why system (1) where K is kinetic energy, Uis potential energy, and Wis work. In this experiment, the initial elastic potential energy of a spring and gravitational potential energy of a block launched down a ramp are converted into kinetic energy and then into thermal energy as the block slides to a stop as a result of friction. When an object slides along a surface, it is subjected to a frictional force which opposes its motion. This frictional force can be expressed as: FFR : (-1ka (2) where at is the coefcient of kinetic friction, m is the mass ofthe object, and g is acceleration due to gravity. When an object is pushed or pulled along a horizontal surface at a constant velocity, Newton's rst law of motion tells us that the net force on the object must be equal to zero (otherwise it would be accelerating). The force that balances the applied force (Rum) in the horizontal direction is the frictional force (Fm) between the object and the surface. FAPP: Fr-'s (3) As the forces are balanced in the vertical direction, the normal force is equal to mg. Determination of the coefcient of kinetic friction \"5'1 1. 2. 3. 4 10. 11. 12. 13. Click on the \"Coefficient of kinetic friction\" tab in Capstone. Weigh the red cart and block and record this value in Table 1 on the proforma. Clean dust and grit from the block and the track with a so cloth. Place the red cart on top ofthe friction block with the felt side down and the plunger directed away from the motion sensor. Place the blue cart on the track with its wheels in the grooves and the rubber bumper ofthe force sensor directed away from the motion sensor, as shown in Figure l (a). With the rubber bumper not touching anything, push the \"ZERO\" button on the force sensor and then position the rubber bumper so that it is near the rear ofthe red cart. Click RECORD I in Capstone and gently push the force sensor on the blue cart against the protruding part ofthe block holder so that the block and two carts move along the track at a constant velocity. Ensure that the block travels parallel to the grooves in the track. Click STOP I. In Capstone, examine the plot of velocity vs time and find an interval over which the graph is horizontal. Then, click to select data from the plot of force vs time and zoom to that same interval. Use the data highlighter tool .1; to highlight the data recorded over that interval, click the pull-down arrow by the Statistics I ' icon and select \"Mean\Figure l , (a) the red cart has a friction block as its base, while a force sensor is mounted on the blue cart and (b) the cork friction block. Method Determination of the spring constant {k} of the plunger 1. Open the Capstone file \"Mechanical to Thermal Block on Ramp\" then click on the \"Spring constant\" tab. 2. Fully depress the plunger of the red cart with your nger and ensure that it restores to its full extension when you remove your nger. If it gets stuck, ask your demonstrator for assistance. Do not touch the sticky tape that covers the button on the top of cart. 3. Place the red cart on the track with its wheels in the grooves and the plunger directed away from the motion sensor. The block holder and block should be placed in the top of the cart, with the protruding section ofthe holder at the rear of the cart. 4. Place the blue cart on the track with its wheels in the grooves and the rubber bumper of the force sensor directed away from the motion sensor. 5. With the rubber bumper not touching anything, push the \"ZERO\" button on the force sensor and then position the rubber bumper so that it is near the protruding section of the block holder on the red cart. 6. Click RECORD I in Capstone and push the blue cart against the red cart so that that the force sensor pushes against the block holder until the plunger has been fully depressed. This should be done in one smooth motion. Press STOP I. 7. Examine the graph of Force (F) vs position (x). The change in position of the block and cart is equal to the compression of the plunger, 3;. Record this value in the relevant section of the proforma. 8. Plot F vs x and then click E to pull up the curve t function and select \"Linear\" in order to t a straight line to your data. Use the data highlighter tool :43" to highlight the data that you want to consider and record the slope of the line as k on your proforma. 9. Collect three values for k and then calculate an average value for k. Question 3 Draw a free body diagram of the block and red cart (treated as a single mass) when they are being pushed at a constant velocity (described in Part B - Step 7 of the instructions). Free body diagram 0.5 0Risk Assessment Risk assessment is extremely important in engineering. It is your job as engineers to identify and understand the risks present and to suggest measures to prevent harm from happening. Risks are assessed using the matrix below. The two main criteria used are likelihood of occurrences and severity of consequences, outlined in the table below. Risks are mitigated through a hierarchy of controls. Consequences Likelihood Insignificant Minor Moderate Major Catastrophic Almost Certain - Expected in most Low + Moderate + High Very High Extreme circumstances Likely - Will probably occur in most Low - Moderate - Moderate + High Very High circumstances Possible - Might occur at some time Negligible Low - Moderate - Moderate + High Unlikely - Could occur at some time Negligible Low - Low + Moderate - Moderate + Rare - May occur only in exceptional Negligible Negligible Negligible LOW - Low + circumstances Consequences How severely could it hurt someone/cause damage? Catastrophic Death or large number of serious injuries, environmental disaster, huge cost Major Serious injury, extensive injuries, severe environmental damage, major cost Moderate Medical treatment required, contained environmental impact, high cost Minor First aid treatment required, some environmental and/or financial impact Insignificant No injuries, low financial/environmental impact Risk score What should I do? Extreme Immediate action required Very High Senior management attention required High Action plan required, senior management attention needed Moderate Specific monitoring or procedures required, management responsibility must be specified Low Manage through routine procedures Negligible Accept the risk Hierarchy of Controls Elimination Physicaly remove the hazard Substitution Replace the hazard Engineering Isolate people Controls from the hatand Administrative Change the way Controls | people work PPE Protect the worker with Personal Protective Equipment LameThe amount of energy lost by the object in the form of thermal energy (heat), which is equal to the work done against the object by friction, is given as: WZFp-R s (4) where s is the displacement ofthe object. In this experiment, a spring does work on the block and cart. The compression or stretch of an ideal spring is directly proportional to the force that the spring exerts: 1?:ch (5) where k is the spring constant and x is the distance that the spring is compressed from its equilibrium. When work is done on a Spring, the work is stored as elastic potential energy, which can then be used to do work on an object. This work is given as: W=ikx3 (6) Analysis ofthe different forms ofenergy present in the system gives: Elastic P.E. + gravitational P.E. = work done against friction = thermal energy lost By identifying the forces acting on the block as it slides down the ramp, it can be shown from the previous equations that the values in this energy statement can be calculated using: kxz + mg 3 SW? = pkmg s c059 (7) where k is the spring constant ofthe plunger, x is the distance by which the plunger is compressed, or is the mass ofthe friction block plus the cart, s is the distance that the block slides after the plunger is released, and E} is the angle of the ramp with respect to the horizontal