70 University of South Alabama Physics PH 201/PH 202 Laboratory Manual 6.5 Preli

Question

70 University of South Alabama Physics PH 201/PH 202 Laboratory Manual 6.5 Preliminary Assignment 1) Consider an object that moves only along the positive X axis that is subjected to a constant force pointing in the positive X direction. Show the work done by this force is the area under a Force vs. Displacement plot. 2) A cart of mass (851.8±0.1) g is configured in a setup as shown in Figure 6.4.1. The tension in the string is 0.36 N and the cart has a displacement of 40.9 cm. Determine the work done by the tension. 3) The cart in the previous example has a maximum velocity of (0.580±0.017) % . Determine the kinetic energy of the cart and compare the result with the work done on the cart in Problem 2 to confirm the Work-Energy Theorem.

Explanation / Answer

1. consider an object subject to only force in x direction and it can move only in x direction

work done b y this force at time t to move object furhter by distance dx

dW = Fdx

total work = integrate[Fdx]

but this integration is area under the force displacement curve

hence

work done by the force is area under force displacement curve

2. mass of cart m = 851.8+-0.1 g

tension in string, T = 0.36 N

displacement of cart d = 40.9 cm

work done by tension = Td = 0.36*40.9/100 = 0.14724 J

3. Vmax = 0.58+-0.017 m/s

KE of the cart at this point = 0.5mv^2 = 0.5*0.58^2*0.8518 = 0.14327276 J

so this KE and work done by temnsion are approimately equal and hence conforming to the work energy theorem

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