PhysicsLab3

Physics 114 6/03/19 Karl Hou, Meredith Strickler, Jaylin Hardy, Dan Redler, Han Duong Formal Lab: Dynamic Mass Intro: In this lab our groups aim is to dynamically measure the lab carts mass using N2L, then compare our experimental value to the measured value. Our lab will be successful if both values are in agreement. Purpose: The purpose of this lab is to determine the mass of a cart and a brass hanger directly (using a triple beam balance) and indirectly (calculated using force and motion sensors), and then to compare these two measurements with each other. Procedure: Lab Set-up:  Attach sensor to to the top of the cart, then place the cart on the track attached to a weighted pulley.  Place the cart with the attached pulley on the end of the track, the car will move away from the sensor.  Plug in the LabPro and open software. Adjust force to 10N. Gathering Data:  Measure the uncertainty of the triple beam balance, then measure the mass of the car with the sensor.  Alleviate tension on the pulley and zero (0.00N) the sensor before each run.  Run 8 trails, collect data. Ensure the the constant force and constant acceleration is evident on the graph. The 8 trials is where there was some difficulty collecting data. It was hard to initially get an accurate reading from the sensor. We have to take care that there was no hands or people in range of the sensor. If there were people moving with in range it obscured the measurement of the car.  Each run will produce average acceleration and its standard deviation, and average force and its standard deviation (32 numbers recorded in total). Theory: To determine the dynamic mass (m ) of the the cart and the hanger, we are using the formula F net force = m*a , where F net force is the total force acting on the object, m is the mass of the object, and a is the acceleration of the object. By substituting the force (N) into F net force and the acceleration(m/s 2 ) into a from the experimental data that we collected into the formula, we can calculate the dynamic mass of the brass hanger and the cart. By then we have the equation: m = F net force / a Free Body Diagram:

Mass of the Cart m cart = - T / -a Horizontally, normal force and gravitational force are exerting 0 force on the cart, so in the formula, only Tension (T ) is exerting force on the cart horizontally but Tension force direction is to the left, so there is a minus sign in front of its magnitude. Acceleration here is negative because the cart is accelerating to the left. Therefore: m cart = T / a Mass of the Hanger m hanger = (+T-Fg) /-a Vertically, only Tension force ( T) and gravitational force (Fg) act on the hanger. The tension is pulling the hanger up so its magnitude has a positive sign while the gravitational force is pulling it down so is magnitude has a minus sign. m hanger calculated above since F G , where m is the mass of the cart and g is the gravitational force of exerted by the Earth onto the cart. Therefore: m hanger *(-a) = T - m hanger *g Here, m hanger is the mass of the hanger, a is acceleration. Here acceleration is negative because the hanger is falling down. T is the tension exerted by the string onto the hanger, and g is the gravitational force exerted by the Earth onto the hanger. m hanger *(- a) + m hanger *g = T m hanger *( -a + g) = T m hanger = T /(-a+g) Data: Class’s masses for a single object (stapler): 349.8g, 350.0g, 350.0g, 351.7g, 350.5 Average mass of stapler: 350.4g Average deviation for mass of stapler: 0.56g

Percent uncertainty of triple beam balance=0.56g/350.4g If we multiply this percent uncertainty by the measured mass of our hanger we can get its uncertainty: Measured mass of hanger=50.52g ±0.56g/350.4g*50.52g= 50.52g±0.08g While we were measuring the mass of our cart there was a cord attached to it that had to be carried which would affect our mass measurement. To compensate for this, we decided to add 1.0 g to the uncertainty: Measured mass of cart=345.7g ±(0.56g/350.4g*345.7g)+1g= 345.7g±1.6g Now for our calculated masses using Tension and Acceleration: Using our equations from the Theory section we know m cart = T / a and m hanger = T /(-a+g). And from our data section, we know T=0.3979428571 N ± 0.0259614286 N and a=1.088614286 m/s 2 ± 0.06681 m/s 2 . So, plug these values into our equations to get the masses of the two objects and their uncertainties: Calculated mass of cart = T/a = (0.3979428571 ± 0.0259614286) N/(1.088614286 ± 0.06681) m/s 2 = (0.3979428571 ± 6.523908681%) N/(1.088614286 ± 6.137159953%) m/s 2 = (0.3655499126±12.66106863%) kg = (0.3655499126±0.0462825253) kg = (365.5499126±46.2825253) g = 360g±50g (round to one sig fig in uncertainty) Calculated mass of hanger = T /(-a+g) = (0.3979428571 ± 0.0259614286) N/ (9.8 m/s 2 - (1.088614286 ± 0.06681) m/s 2 ) = (0.3979428571 ± 0.0259614286) N/ (8.711385714 ± 0.06681) m/s 2 = (0.3979428571 ± 6.523908681%) N/ (8.711385714 ±0.7669273545%) m/s 2 = (0.0456807757± 0.0033305105) kg = ( 45.6807757± 3.3305105) g = 46g ± 3g (round to one sig fig in uncertainty) Conclusion: