Purpose: Find the relationship between work done by force and the kinetic energy, and find the spring constant of the spring.
Model: ΔW=ΔKE, W=Fx, KE=(mv^2)/2, and F=kx.
W is the work done on cart by force, KE is the kinetic energy of the cart, m is the mass of the cart, the velocity of the cart, k is the spring constant.
Process: First, we set up the apparatus as showed on picture. We placed the ramp on the horizontal table, and we put the motion detector on one side of the ramp and the force sensor on the other side of the ramp. We put the cart on the ramp, and then we collect the cart and the force sensor by using a spring. The spring needed to be kept on horizontal.
We measured the mass of the cart m. m=0.71kg. We opened the LabPro, calculated the force sensor, and zero the force sensor and the motion sensor. Then, we created the new calculated column for the kinetic energy, KE, by using KE=(mv^2)/2 and the work, W, by using W=Fx.
We pull the cart toward the motion detector, started collecting the datas, and let the cart go.
Then, we got the graph:
We selected the part of the graph that we needed and used the integration routine to the Force vs. Position.
We chose x=0.243m W=0.3297J KE=0.318J
x=0.190m W=0.4614J KE=0.427J
x=0.130m W=0.5662J KE=0.506J
The W is very similar to KE, but they still have some difference, This error may cause by the work done by friction.
By reading the slope of Force vs. Position, k=11.64N/m.
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