A foam cube bounces to a height of 15cm when dropped from a height of 100cm. To what height will it bounce if dropped from a height of 2.5cm?
How do
Is this question answerable????????
please help fast
we solve this problem?
To find the height to which the foam cube will bounce when dropped from a different height, we can use the concept of the energy conservation principle. According to this principle, the potential energy of an object at a certain height is transformed into kinetic energy when the object falls. And when the object bounces back, the kinetic energy is converted back into potential energy.
To solve this problem, we need to understand the relationship between potential energy and height. The potential energy of an object at a certain height is given by the formula:
Potential energy = mass × gravity × height
However, in this problem, we are considering a foam cube, which has a constant mass regardless of its height. Therefore, we can disregard the mass and simplify the formula to:
Potential energy = gravity × height
Now, let's solve the problem step by step:
1. Calculate the potential energy of the foam cube when it is dropped from a height of 100cm:
Potential energy = gravity × height
Potential energy1 = 9.8 m/s² × 100cm = 980 J (Joules)
2. Since the foam cube bounces back to a height of 15cm, we can assume that the potential energy after the bounce is equal to the potential energy before the drop (assuming no energy is lost to other factors like air resistance or deformation). So the potential energy after the bounce is also 980 J.
3. Now, we can use the potential energy formula to find the height to which the foam cube will bounce when it is dropped from a height of 2.5cm:
Potential energy = gravity × height
Potential energy2 = 9.8 m/s² × height2
Since the potential energy before and after the bounce is the same, we can equate the two potential energy values:
Potential energy1 = Potential energy2
980 J = 9.8 m/s² × height2
4. Rearranging the equation to solve for height2:
height2 = 980 J / 9.8 m/s² = 100cm
Therefore, the foam cube will bounce back to a height of 100cm when dropped from a height of 2.5cm.