A group of students performing Newton\'s Second Law experiment generated the gra

Question

A group of students performing Newton's Second Law experiment generated the graph shown below from their data. Which of the following statements is true regarding the trustworthiness of the data? (Select all that apply.) http://www.webassign.net/ncsuplsemech2/3-post-002.GIF 1)The graph should have a positive y-intercept because a certain amount of mass is needed on the hanger to overcome the friction and create a net force in the forward direction. 2)The negative y-intercept indicates the amount of friction force present. 3)Friction would cause the plot to be shifted upward such that the y-intercept is positive. Therefore the negative y-intercept indicates incorrect data. 4)The graph crossing the x-axis at some positive value of the acceleration indicates the presence of a non-zero acceleration, which is in agreement with Newton's Second Law. 5)The plot of the data crosses the x-axis at a positive value of the acceleration. This means that when the hanging mass is zero, the cart still has some acceleration, which seems contrary to Newton's Second Law. 6)The track was not level and the cart went downhill during the experiment, causing the cart to accelerate in the forward direction even when the hanging mass was zero.

Explanation / Answer

Since there’s no description about the actual experimental setup, I’ll make the guess that the experiment is about a cart on a level track being pulled by a hanging mass at one end of the track. The force equation is then given by …… T – f = m2 a …… where …… T = tension in the string …… f = friction … m2 = mass of the cart …… For the hanging mass m1 …… m1 g – T = m1 a ---> T = m1 g – m1 a …… Combining the two force equations …… [ m1 g – m1 a ] – f = m2 a …… … m1 g – f = [ m1 + m2 ] a …… by varying the hanging mass m1 , different accelerations are obtained. Making the following replacement of variables … m1 g ---> y …… a ---> x …… the combined force equation can be rewritten as …… y – f = [ m1 + m2 ] x ---> y = [ m1 + m2 ] x + f …… which has the form of the standard equation of a straight line y = s x + p , where s = slope of the line and p = y intercept …… • … Since f is the magnitude of frictional force in y = [ m1 + m2 ] x + f , f there is already positive so the plot should have a positive y intercept, not negative. Statement A is therefore true. • … If the hanging mass were at the right end of the track, the cart would then be pulled to the right also, so that friction is to the left. This is the case that gives a positive y intercept. A negative y intercept would then mean friction in the opposite direction, meaning to the right, so that the cart should be moving to the left, opposite to the direction the hanging mass is pulling. That would mean that the track is not purely horizontal but inclined backward., not forward. The cart would then accelerate in the backward direction with no hanging mass. Statement B is therefore false. • … C is true. • … D is false. There’s no contradiction with Newton’s second law. The equation y = [ m1 + m2 ] x + f = m1 g was set up on the premise that the cart will move so friction is present. It cannot be applied when friction is absent. • … E is true. • … The graph crossing the x-axis means y = m1 g = 0 , so that m2 x + f = 0 ---> f = m2 a = - m2 x ? 0 ---> a ? 0 ---> F is true

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