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Download Newton`s Second Law Purpose: Investigate Newton`s Second Law
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Transcript
Newton’s Second Law Purpose: Investigate Newton’s Second Law of Motion Concept and Skill Check Newton’s second law of motion states that the acceleration of a system is directly proportional to the net force on it and inversely proportional to its mass. In mathematical form, this law is expressed as a= F/m. An object will accelerate if it has a (net external) force acting on it, and the acceleration will be in the direction of the force. In this experiment, a laboratory cart will be accelerated by a known force, and its acceleration will be measured using a motion sensor and computer. The product of the total mass accelerated and its acceleration equals the force causing the acceleration. In order to calculate the net force acting on the laboratory cart, frictional forces that oppose the motion must be offset. If the cart moves at a constant velocity, then the net force acting on the cart is zero because the acceleration is zero. The frictional force can be neutralized by providing enough small masses at the end of the string to make the cart move forward at a constant velocity. If you assume that the laboratory cart experiences a uniform acceleration due to the falling mass, then the relation ship d = vit + ½ a t2 applies. If the cart has an initial velocity of zero, the equation becomes d = ½ a t2 If the displacement in a given time is known, you can solve for the acceleration with a = 2 d/t2 Materials Computer, Motion sensor , Data Studio software, mass sets with hangers and paper clips for fine mass adjustments, heavy string (1.5m), triple beam balance, dynamics cart, track, meter stick or track with measurements for distance. Procedure 1. Determine the combined mass of your dynamics cart and string and any masses riding on top of the cart. Record the mass in Table 1. 2. Assemble the cart, pulley, motion sensor as shown in Figure 1 on the next page. (Modifications will be made if your equipment is different than the picture.) Tie a small loop in the end of the string hanging from the pulley. 3. Give the cart a small push. It should roll to a stop in a few centimeters. Attach a small mass (paper clips or plastic “hanger assembly”) to the end of the string that is hanging from the pulley. Give the cart a small push toward the pulley and observe its motion. If the cart moves a constant velocity then the weight of the mass is equal to the force of friction in the cart’s wheels and from the any other sources of friction. If the cart rolled to a stop, then the total mass on the string must be increased. If the cart’s velocity increased after it was released, then the total mass on the string must be decreased. Adjust the total mass until the cart moves a constant velocity after you have given it a small push. Record in Table 1 the mass needed to equalize the friction of the cart. Leave the small masses attached to the string. Take a screen shot of your computer using the Print Screen function or the Snipping Tool to submit with your lab. 4. Now you are ready to accelerate the system. Start by adding about 50 grams to the hanging mass that you just used to neutralize the friction in the system. Record the total of these masses in Table 2 under Trial 1. Determine acceleration with two methods. You should perform these as the same time. In the first, use DATA Studio to determine the acceleration of the system. Move the cart next to the motion sensor. Adjust the string length so that the mass is hanging just under the pulley. Hold the cart to prevent it from moving. Turn on the motion sensor. Release the cart, allowing it to accelerate across the track. Catch the cart before it collides with the pulley or plunges to the floor. Turn off the motion sensor. Record your data in table 3. For the second method use a stop watch and the formulas described at the beginning of the lab. Record your values in Table 4. Calculate the acceleration and compare it to that of the computer. 5. Repeat steps 5 and 6 twice more for a total of three trials. Use different masses for different accelerations of the system. Do not exceed 150 grams. Observations and Data Table 1 Value (kg) Mass of laboratory cart with any riding weights Mass needed to equalize friction of cart Force of Friction (N) Table 2 Trial Hanging Mass (kg) Accelerating force (N) Force of Friction (N) From table 1 FNET (N) 1 2 3 Table 3 Trial Mass of laboratory cart with any riding weights from table 1 (kg) Hanging Mass from table 2 (kg) Total mass of system (kg) Acceleration calculated by computer (m/s2) 1 2 3 Table 4 Trial 1 2 3 Total mass of system (kg) from table 3 Stop watch time (s) Displacement (m) Acceleration calculated by you (m/s2) (msystem) *(a) (N) Analysis: All values that have been calculated and inserted into the above tables must be shown here. Use a working equation, show algebra if relevant and finally substitutions and box your final answers. 1. Show calculations for the frictional force along with a free body diagram of the cart. This diagram refers to the cart moving at constant velocity. Forces are balanced or said to be in equilibrium. 2. Show calculation for the accelerating force. 3. Why was it important to neutralize the effect of friction force acting on the system? 4. Are your acceleration values less than, equal to or greater than g? Are these the values you would have predicted? Explain. 5. The total mass that was accelerated is equal to the mass of the cart, string, the riding weights if you used them, the small masses need to equalize friction, and the hanging mass. Calculate the total mass of your system and record this value in t Table 3 6. Calculate the product of the total mass and the acceleration for each trial using the computers values of acceleration. Record these values in Table 3. 7. Calculate the product of the total mass and the acceleration for each trial using your stopwatch-derived values of acceleration. Record these values in Table 4. Compare the values and comment. 8. Compare the results for the product (m) (a) to the accelerating force. Find the relative error using the accelerating force as the reference value. 9. Based on your answers for # eight. Have you succeeded in verifying Newton’s Second law? Why or why not? Comment. Application At a specific engine rpm, an automobile engine provides a constant force that is applies to the automobile. IF the car is traveling on a horizontal surface, does the car accelerate when this force is applied? Explain.