A .50kg rock is tied on a 1.0 m string which has a breaking force of 990 N . If the string breaks, what is the speed of the rock? Show ALL work in the space provided.

To find the speed of the rock at the moment the string breaks, we need to determine the force exerted on the rock and the acceleration caused by that force. First, we can use Newton's second law: \[ F = ma \] where \( F \) is the net force applied to the rock, \( m \) is the mass of the rock, and \( a \) is the acceleration. Given that the mass \( m \) of the rock is 0.50 kg and the breaking force \( F \) is 990 N, we can rearrange the equation to solve for acceleration: \[ a = \frac{F}{m} = \frac{990 \, \text{N}}{0.50 \, \text{kg}} = 1980 \, \text{m/s}^2 \] Now, if we assume that the rock was initially at rest and we want to find the speed \( v \) at the moment the string breaks, we can use the Kinematic equation: \[ v^2 = u^2 + 2as \] where \( v \) is the final speed, \( u \) is the initial speed (0 m/s in this case), \( a \) is the acceleration (1980 m/s²), and \( s \) is the distance (1.0 m in this case). Now we can plug in the values: \[ v^2 = 0 + 2 \times 1980 \, \text{m/s}^2 \times 1.0 \, \text{m} \] \[ v^2 = 3960 \, \text{m}^2/\text{s}^2 \] \[ v = \sqrt{3960} \approx 63.0 \, \text{m/s} \] Thus, if the string breaks, the speed of the rock at that moment would be approximately **63.0 m/s**.