Question

The mass of the cart is 0.365 kg. The rest of the data can be obtained from the graph above. All answers below must be correct to 3 significant figures. Units are required if not stated. What the final speed of the cart predicted by the work done by the rubber band, assuming that friction negligible? Vpred What the percent difference between between the predicted and measured final speed, expressed as a percent of the measured speed? Percent difference between vored and vmeas Assume that the difference between the measured and predicted speeds is due o friction loss. Base on this, how much energy is lost to friction these measurements? AEr Finally, assuming that the friction force is constant over the displacement, what is the average magnitude of the friction force on the cart? Average Fr F&y YS. x X A Fit Data - 0 434 1.8 1,6 Run #3 1.4 1.2 1.0 1.81 0.8 0.6 0.4 0.2 (0.176, 0.00) 0.0 0.4338 0.0 Area -0.5 Run#3 -0.78 N m -1.0 1.5 -2.0 4,07 -2.5 -3.0 -3.5 r 0.1761,-4.05) -4,0 0.20 0.30 0.40 0.50 0.60 0.70 0.80 Position, Ch 1&2(m) Force, Ch A( N) + Velocity, Ch 1&2( m/s) +

Answer 1

given m = 0.365 kg

from graph work done is = 0.78 N-m

$\Delta$ KE = W

initial speed is V_i = 0

0.5 x m ( V_f² - V_i² ) = W

0.5 x 0.365 x ( V_f² - 0 ) = 0.78

V_f = 2.067 m/sec

so

V_pred = 2.067 m/sec

from graph,

V_meas = 1.8 m/s

V_pred = 2.067 m/s

% difference = ( V_pred - V_meas ) x 100 / ( V_pred + V_meas / 2 )

% difference = ( 2.067 - 1.8 ) x 100 / ( 2.067 + 1.8 / 2)

% difference V_meas= 8.99

$\Delta$E_f = 0.5 m ( V²_pred - V²_meas )

$\Delta$E_f = 0.5 x 0.365 x ( 2.067² - 1.8² )

$\Delta$E_f = 0.188 J

we have equation for work is " W "

W = F_f x

0.188 = F_f x 0.434

F_f = 0.188 / 0.434

average F_f = 0.4331 N