Kinematics
Equation 1: xf=xi+vit+1/2at^2
77.545 = 0.00 + 0(1.2) + (1/2)a(1.2^2)
77.545 = (1.44)a/2
a = 107.701 cm/s^2
a=1.077 m/s^2
Equation 2: vf^2= vi^2+2aDeltax
Vf^2 = 0 + 2(107.701)(77.545)
Vf = 129.2414 cm/s
Vf=1.2924 ms
Equation 3: vf=vi +at
Vf = 0 + 1.2(107.701)
Vf = 1.29212 m/s
77.545 = 0.00 + 0(1.2) + (1/2)a(1.2^2)
77.545 = (1.44)a/2
a = 107.701 cm/s^2
a=1.077 m/s^2
Equation 2: vf^2= vi^2+2aDeltax
Vf^2 = 0 + 2(107.701)(77.545)
Vf = 129.2414 cm/s
Vf=1.2924 ms
Equation 3: vf=vi +at
Vf = 0 + 1.2(107.701)
Vf = 1.29212 m/s
This velocity vs. time graph shows us how the velocity changes as the time increases. As you can see the velocity of the cart increases as the time increases due to gravity. This graph is supposed to be mostly like a line but due to Trackers frame deletion the graph drops a few times.
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This position vs. time allows us to see how the cart moves position wise verses how much time is going by. You can see that as the time increases the position of the cart also increases because gravity is pushing the cart down to a new position on the ramp.
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Forces
Newtons second law of motion states that acceleration occurs when a force is applied to something. So the greater the mass of the object the more force is needed to accelerate the object. This law can also be put in the formula F=ma.
This applies to the cart because the force applied to the cart by gravity can be figured out if you know whats the mass and acceleration of the cart. Take for example the cart is 5.95 kilograms and the cart accelerates at 107.70 centimeters per second. Then the force applied to the cart is 640.815 newtons of force.
Newtons second law of motion states that acceleration occurs when a force is applied to something. So the greater the mass of the object the more force is needed to accelerate the object. This law can also be put in the formula F=ma.
This applies to the cart because the force applied to the cart by gravity can be figured out if you know whats the mass and acceleration of the cart. Take for example the cart is 5.95 kilograms and the cart accelerates at 107.70 centimeters per second. Then the force applied to the cart is 640.815 newtons of force.
This is a free body diagram of the cart rolling down the ramp with the three main forces acting here. The three forces in this instance are the table, gravity, and friction.
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So since the brown box represents the cart the forces on the cart are these four basic forces. The first force is pushing the cart down and to the right and it is weight which is how much gravitational force is being applied to the cart and so in this case is 9.8 meters per second. The second force is the normal force supporting the cart from falling straight down and in this case is the table. The third force is the original force pushing the cart to the right and in this case is Mr. Lamee's hand. The fourth and final force is friction and it doesn't affect the cart much but it's friction and it push's the cart to the left.
F=ma F=0.596(1.077) F= 0.64189 N |
Energy
Equation 1 KE=1/2mv^2
KE= 1/2(0.595)1.292412^2
KE=0.496922 J
Equation 2 PE=mgh
PE=(0.595)(9.8)(0.0762)
PE= 0.4443222 J
But the way the potential energy becomes kinetic energy is through the law of conservation of mass. When the potential energy of the cart on top of the ramp becomes kinetic energy going down the ramp the energy is never lost between the transfer of energy's. This is because the law of conservation of mass states that energy can not be created nor destroyed but only transformed form one type of energy to another.
Equation 1 KE=1/2mv^2
KE= 1/2(0.595)1.292412^2
KE=0.496922 J
Equation 2 PE=mgh
PE=(0.595)(9.8)(0.0762)
PE= 0.4443222 J
But the way the potential energy becomes kinetic energy is through the law of conservation of mass. When the potential energy of the cart on top of the ramp becomes kinetic energy going down the ramp the energy is never lost between the transfer of energy's. This is because the law of conservation of mass states that energy can not be created nor destroyed but only transformed form one type of energy to another.
This graph is showing the time vs. kinetic energy of the cart going down the ramp. So obviously when the cart goes down the ramp the time increases and with it the kinetic energy also increases as the potiental energy decreases because of the height lose.