Chapter 5, Problem 88AP

An object of mass m is suspended from the top of a cart by a string of length L as in Figure P5.88a. The cart and object are initially moving to the right at a constant speed υ₀. The cart comes to rest after colliding and sticking to a bumper, as in Figure P5.88b, and the suspended object swings through an angle θ. (a) Show that the initial speed is ${\upsilon }_0=\sqrt{2gL(1-\cos \theta )}$. (b) If L = 1.20 m and θ = 35.0°, find the initial speed of the cart (Hint: The force exerted by the string on the object docs no work on the object.)

  

  Figure P5.88a