1. A 0.50 kg fan cart is placed on a level, horizontal track of negligible friction, as shown. The fan is turned on,and the fan cart is released from rest and moves to the right. The cart travels along the horizontal track and then down an incline. Motion detector 1 measures the acceleration a of the cart from time t=0 to t=3s. At t=3 s, the cart makes a smooth transition to the incline, and motion detector 2 measures the acceleration of the cart after t=3 s. The fan exerts the same magnitude of force on the cart during the entire motion. The graphs below show a as functions of t. For each motion detector, the positive direction is away from the detector.
(a) On the dots below that represent the cart at two different locations, draw and label the forces (not components) that act on the cart at each location. Each force must be represented by a distinct arrow starting on, and pointing away from, the dot.
(b) Calculate the magnitude of the net force exerted on the fan cart when it is on the horizontal track.
(c) Calculate the angle q of the incline.
(d) Suppose careful measurement determines the angle of the incline to be 3° larger than that calculated in part (c). Consider the following explanation.
“The scale used to measure the mass of the fan cart was not calibrated properly before the measurement, and
this could account for the observed difference in the angle.”
Does the explanation sufficiently account for the observed discrepancy?
_____ Yes _____ No
Justify your answer.
The experiment is repeated for several trials, each with a different angle for the incline. The acceleration of the cart down the incline is measured for each angle. The graph below shows the plot of the acceleration a of the cart as a function of the sine of the angle sin θ.
i. Draw a best-fit line for the data.
ii. Using the straight line, calculate an experimental value for the acceleration due to gravity g.
(f) If the cart were replaced with a second cart of mass 1.0 kg that has a fan that exerts the same magnitude of force as the original fan, explain how the graph given in part (e) would change.