A chicken's egg of mass 58 g is dropped onto grass from a height of 1.1 m. Assume that air resistance is negligible and that the egg does not bounce orbreak.a. Define impulse.[1]b.i. Show that the kinetic energy of the egg just before impact is about 0.6 J.[1]b.ii.The egg comes to rest in a time of 55 ms. Determine the magnitude of the average decelerating force that the ground exerts on the egg.[4]b.ii Explain why the egg is likely to break when dropped onto concrete from the same height.
Question
A chicken's egg of mass 58 g is dropped onto grass from a height of 1.1 m. Assume that air resistance is negligible and that the egg does not bounce orbreak.a. Define impulse.[1]b.i. Show that the kinetic energy of the egg just before impact is about 0.6 J.[1]b.ii.The egg comes to rest in a time of 55 ms. Determine the magnitude of the average decelerating force that the ground exerts on the egg.[4]b.ii Explain why the egg is likely to break when dropped onto concrete from the same height.
Solution
a. Impulse is defined as the change in momentum of an object when a force is applied over a period of time. It is calculated as the product of the force and the time over which the force is applied.
b.i. The kinetic energy of the egg just before impact can be calculated using the formula for kinetic energy, which is KE = 1/2mv^2. However, we don't know the velocity of the egg just before impact. We can find this using the equation of motion v^2 = u^2 + 2as, where u is the initial velocity, a is the acceleration due to gravity, and s is the distance fallen. The initial velocity u is 0 (since the egg is dropped, not thrown), a is 9.8 m/s^2, and s is 1.1 m. So, v^2 = 0 + 29.81.1 = 21.56 m^2/s^2. Therefore, v = sqrt(21.56) = 4.64 m/s. Substituting m = 58 g = 0.058 kg and v = 4.64 m/s into the formula for kinetic energy gives KE = 1/20.0584.64^2 = 0.62 J, which is approximately 0.6 J.
b.ii. The decelerating force can be found using the formula for impulse, which is Impulse = Force * time = change in momentum. The initial momentum is mv = 0.058 kg * 4.64 m/s = 0.269 kgm/s. The final momentum is 0 (since the egg comes to rest). So, the change in momentum is 0 - 0.269 kgm/s = -0.269 kgm/s. The time over which this change occurs is 55 ms = 0.055 s. Therefore, the average force is Impulse/time = -0.269 kgm/s / 0.055 s = -4.89 N. The negative sign indicates that this is a decelerating force.
b.iii. The egg is likely to break when dropped onto concrete from the same height because concrete is a much harder surface than grass. When the egg hits the concrete, the decelerating force is applied over a much shorter period of time, resulting in a much larger force and therefore a greater chance of the egg breaking.
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