Physics Answers

In a laboratory experiment, you wish to determine the initial speed of a dart just after it leaves a dart gun. The dart of mass ##m## is fired with the gun very close to a wooden block of mass ##M_0## which hangs from a cord of length ##l## and negligible mass as shown below. Assume the size of the block is negligible compared to ##l## and the dart is moving horizontally when it hits the left side of the block at its center and becomes embedded in it. The block swings up to a maximum angle ##\theta_{max}## from the vertical. Express your answer to the following in terms of ##m## , ##M_0## , ##l## , ##\theta_{max}## , and ##g## .
C. The dart is now shot into a block of wood that is fixed in place. The block exerts a force F on the dart that is proportional to the dart’s velocity v and in the opposite direction, that is F = -bv, where b is a constant. Derive an expression for the distance L that the dart penetrates into the block in terms of m, ##v_0## , and b.