2 BOOKS
Kinematics:
Three Kinematic Equations:
Three Kinematic Equations:
- Xf = Xi + Vit + 1/2at^2
- 0.26 = 0 + 2(0) + 1/2(2^2)a; a = 0.13 m/s
- Vf = Vi + at
- 0.26 = 0 + 2(a); a = 0.13 m/s
- Vf^2 = Vi^2 + 2a(delta)x
- 0.26^2 = 0^2 + 2a(0.26); a = .13 m/s
![Picture](/uploads/3/8/0/3/38031029/445519_orig.jpg)
Velocity vs. Time
![Picture](/uploads/3/8/0/3/38031029/9150016.jpg?934)
Position vs. Time
Acceleration vs. Time
Text Explanation:
The object observed and analyzed in this lab was a cart with a weight adjusted on top of it, which went down a ramp measuring about 37 centimeters from start to end. By having a downward slope for the ramp, there exists the motion of the cart where it actually accelerated when moving downwards on the ramp, a Acceleration vs Time graph could answer the question of whether the acceleration was nearly constant or varied at different time-frames. But, as seen in the kinematic equations above we can re-arrange the equations to solve for one constant, which in our case was acceleration. Each of the equations can be used to solve different constants, the first equation for example can be used to solve for final position, the second for final velocity, and the third for final velocity squared. The graphs can be used as a guide-way for attaining the answer as Position vs Time graph shows us that the position of the cart steadily increases in our time-frame as the time increases, conveying a positive correlation between the two variables. The Velocity vs Time graph also has an increasing line conveying a positive correlation, meaning that the velocity of the cart increases as it travels down the ramp thus conveying that this is not constant velocity. But, in the Acceleration vs Time graph our acceleration seems to be mostly stable as the cart travels down the ramp, thus signifying a constant variable that will be used in the three kinematic equations.
The object observed and analyzed in this lab was a cart with a weight adjusted on top of it, which went down a ramp measuring about 37 centimeters from start to end. By having a downward slope for the ramp, there exists the motion of the cart where it actually accelerated when moving downwards on the ramp, a Acceleration vs Time graph could answer the question of whether the acceleration was nearly constant or varied at different time-frames. But, as seen in the kinematic equations above we can re-arrange the equations to solve for one constant, which in our case was acceleration. Each of the equations can be used to solve different constants, the first equation for example can be used to solve for final position, the second for final velocity, and the third for final velocity squared. The graphs can be used as a guide-way for attaining the answer as Position vs Time graph shows us that the position of the cart steadily increases in our time-frame as the time increases, conveying a positive correlation between the two variables. The Velocity vs Time graph also has an increasing line conveying a positive correlation, meaning that the velocity of the cart increases as it travels down the ramp thus conveying that this is not constant velocity. But, in the Acceleration vs Time graph our acceleration seems to be mostly stable as the cart travels down the ramp, thus signifying a constant variable that will be used in the three kinematic equations.
![Picture](/uploads/3/8/0/3/38031029/1410479073.jpg)
Forces:
Free Body Diagram of Cart Rolling Down Ramp: The F1 force can be classified as the air resistance/drag/friction working against the cart as it is going down the ramp, the F2 force can be classified as gravity which is acting down upon the cart, and F3 can be classified as the opposing force of the ramp towards the car (Newton's 3rd Law).
Text Explanation:
Newton's 2nd Law of Motion states that Force = Mass (Acceleration), thus we can find out the force (in Newton's) the cart is being acted on when going down the ramp for a given time-frame if we know the mass and relevant acceleration. By using our first equation from the kinematics equations section we can figure out the current acceleration of the cart for a given time-frame, and the mass of both the cart and the weight on it was found to be 597 grams in total. Now, we already know that Force = 0.597a, since mass is supposed to be kilograms and our weight was in grams, thus conversion would take it 0.597 kg. The forces of acting on the cart can be explained by the Free body diagram as to which direction the forces act and which forces they are. Thus, by knowing the given mass of the object and the relevant acceleration, one can figure out the quantity of force in newton's acting on the cart while it travels down the ramp as conveyed by Newton's 2nd Law of Motion where F = MA.
Free Body Diagram of Cart Rolling Down Ramp: The F1 force can be classified as the air resistance/drag/friction working against the cart as it is going down the ramp, the F2 force can be classified as gravity which is acting down upon the cart, and F3 can be classified as the opposing force of the ramp towards the car (Newton's 3rd Law).
Text Explanation:
Newton's 2nd Law of Motion states that Force = Mass (Acceleration), thus we can find out the force (in Newton's) the cart is being acted on when going down the ramp for a given time-frame if we know the mass and relevant acceleration. By using our first equation from the kinematics equations section we can figure out the current acceleration of the cart for a given time-frame, and the mass of both the cart and the weight on it was found to be 597 grams in total. Now, we already know that Force = 0.597a, since mass is supposed to be kilograms and our weight was in grams, thus conversion would take it 0.597 kg. The forces of acting on the cart can be explained by the Free body diagram as to which direction the forces act and which forces they are. Thus, by knowing the given mass of the object and the relevant acceleration, one can figure out the quantity of force in newton's acting on the cart while it travels down the ramp as conveyed by Newton's 2nd Law of Motion where F = MA.
![Picture](/uploads/3/8/0/3/38031029/8736239_orig.jpg)
Kinetic Energy Graph
Energy:
Kinetic Energy:
KE = 1/2(mv^2)
- KE = (at 2.0 seconds (bottom of the ramp)) = (1/2)((.597 kg)(.26 m/s)^2) = 0.0202 Joules (will differ by 2 decimal places)
Gravitational Potential Energy:
- PEg = mgh
- PEg = (at 0 seconds (top of the ramp)) = (0.597 kg)(9.80 m/s^2)(0.0762 m) = 4.37 Joules (will differ by 2 decimal places)
The kinetic energy of the cart increases as the cart travels down the ramp due to the fact that it's velocity increases because of a downward slope of the ramp, whereas the potential energy decreases mostly due to the fact that the height at which the car is, decreases, again because of the downward slope of the ramp, and the mass of the cart remains constant thus allowing for an easy one variable change equation. The Law of Conservation of Energy states that the total amount of energy in a system remains constant, although energy within the system can be changed from one form to another or transferred from one object to another (EnergyEducation: Website). Thus, in this case the energy decreased when the height decreased, decreasing potential energy with it, and in response the kinetic energy increased because velocity of the cart increased as it traveled down the ramp. However, energy was not destroyed/created, it was just converted/transferred from potential energy to kinetic energy; but not all was converted/transferred to kinetic energy, some energy was lost to heat as a result. As can be observed from the Kinetic Energy graph above, that as the cart traveled down the ramp its kinetic energy increased, showing a direct relationship between the two variables.
Website: http://www.energyeducation.tx.gov/energy/section_1/topics/law_of_conservation/