Height of incline. H =17.1 cm Distance between photogates, l = 490 cm Time inter

Question

Height of incline. H =17.1 cm Distance between photogates, l = 490 cm Time interval delta t1 = s Calculation of velocity at position 1, V1 (Can be calculated in cm/s and then convert answer to m/s) : Time interval delta t2 = s Calculation of velocity at position 2, v2: Calculation of the kinetic energy of the cart at position 1, KE1 . Calculation of the kinetic energy of the cart at position 2, KE2 : Calculation of the gain in the kinetic energy of the cart (or change in the kinetic energy of the cart), delta KE: Calculation of height displaced by cart from position 1 to 2, h (in cm and converted to m): Calculation of the loss in the potential energy of the cart (or change in potential energy of the cart), APE: Calculation of the percent difference between the potential energy lost by the cart and the kinetic energy gained by the cart.

Explanation / Answer

Average time interval delta t1 = average of values given in the table belonging to height=17.1cm

Hence Avg delta t1=0.089073cm

For Finding the velocity at position one has many methods:

a)We can find the average of values given in the table as we did for delta t1 or

b)Velocity After delta t1 along an inclined plane will be V=gsin(12)*delta t1

So Avg V1=0.8766m/s

Similary Delta t2 can be found by average as we did for delta t1

Average delta t2 =0.0516533 s

Similarly Average v2=1.51m/s

Average K.E at position 1 =0.28616J

Average K.E at position 2 =0.849J

Change in K.E=Average of values given in table=0.562633J

Height Displaced = 17.10m

Loss of potential Energy=0.611J

% difference = 8.266%

Above values are obtained by finding the averages of values given in the rspective tables:

If u need mathematical derivation of those values its as follows:these values are theoretical values:

For Velocity at v1=gsin(12)*delta t1

For velocity at v2=v1+gsin(12)*delta t2

KE at position 1 will be 1/2*m*v1*v1

KE at position 2 will be 1/2*m*v2*v2

Gain is difference in those values:

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