Question

a cat plays with a toy mouse suspended from a light string of length 1.25 m, rapidly battling the mouse so that it acquires a speed of 2.75 m/s while the string is still vertical. use energy conservation to find the mouse's maximum height above its original position

Answer 1

Using the conservation of energy principle, we calculate that the toy mouse reaches an additional maximum height of 0.387 m above its original position after being hit by the cat and given the initial speed of 2.75 m/s.

Step-by-step explanation:

The question asks for the maximum height achieved by a toy mouse after being hit by a cat, given that the string length is 1.25 m, and the mouse reaches a speed of 2.75 m/s when the string is still vertical. We'll use the conservation of energy principle to solve this problem. At the start, the mouse has kinetic energy due to its speed and potential energy due to its height above the ground. At the highest point of its swing, all the kinetic energy will have been converted into potential energy.

The initial kinetic energy (KEinitial) is given by 0.5 × m × v2 and the potential energy (PEfinal) at the highest point is m × g × h, where m is the mass of the mouse, v is its speed, g is the acceleration due to gravity (9.8 m/s2), and h is the height above the original position. Thus, KEinitial = PEfinal.

Solving for h we get: h = (0.5 × v2) / g. Plugging in the values, we get h = (0.5 × (2.75 m/s)2) / (9.8 m/s2) = 0.387 m. This is the additional height above the original position that the toy mouse achieves before coming to a stop.

Answer 2

As per the energy conversation:

Kinetic Energy = Potential Energy

1/2 x m x v^2 = m x g x h

h = 0.5 x v^2/g

= 0.5 x (2.75 m/s) /9.81 m/s^2

= 0.385 m