3) You tie a small rock of mass m to the end of a string of radius r and start to twirl it about your head. By making your hand move in a very small circle so it is always pulling slightly forward on the rock you are able to continuously apply a force of F to the rock in the tangential direction. Ignore the fact that the rock is always a bit lower than your hand so you can make the approximation that the string is always level. a) Find the linear acceleration of the rock, and find its velocity as a function of time. b) Make a drawing showing the tangential acceleration vector at and any other acceleration vectors. Find the magnitude of the total acceleration of the rock (as a function of time). c) The string breaks when the tension on it exceeds Tm. What would the total acceleration need to be to make it break, in terms of just Tm and m?

3) You tie a small rock of mass m to the end of a string of radius r and start to twirl it about your head. By making your hand move in a very small circle so it is always pulling slightly forward on the rock you are able to continuously apply a force of F to the rock in the tangential direction. Ignore the fact that the rock is always a bit lower than your hand so you can make the approximation that the string is always level. a) Find the linear acceleration of the rock, and find its velocity as a function of time. b) Make a drawing showing the tangential acceleration vector at and any other acceleration vectors. Find the magnitude of the total acceleration of the rock (as a function of time). c) The string breaks when the tension on it exceeds Tm. What would the total acceleration need to be to make it break, in terms of just Tm and m?

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