Question

You create a lab to investigate the concept of work and energy. Figure 1 is a sketch of the experiment setup. The system can be considered frictionless. You have found the combined mass of the cart & force sensor to be 1.20[kg]. The cart is initially at rest. After attaching a 200[g] mass to the end of the string, the cart starts moving. The distance between the floor and the bottom of the hanging mass is initially 80.0[cm]. Assume the acceleration of gravity is 9.81[m/s/s], Calculate the force that you expect will be measured by the force sensor. The mass has now hits the floor. What was the work done by the force on the cart?

Answer 1

a) Here, we see that at intial, mass is hanging and force sensor is not in motion at that instant,

so, F = mg = 0.2*9.81 = 1.962 N

But if we consider that mass m is moving with constant acceleration a .If we draw the FBD for both mass,m and Cart+string (M) and let T be tension in string => T=m(a+g) and T= Ma => a = (mg/M-m) = 0.2*9.81 = 1.962 m/s

And F = (m+M)*a = 1.4*1.962 = 2.7468 N = 2.7 N (approx)

b) Now cart+sensor are in motion.And work-energy say, change in KE = Workdone

mgh = 1/2 m'v²