A lamp hangs from the ceiling at a height of 2.9 m. If the lamp breaks and falls to the floor, what is its impact speed?
Answer (2)
To determine the impact speed of the lamp, we can use the principle of conservation of energy. When the lamp falls from a height of 2.9 m, its potential energy is converted into kinetic energy. The formula to calculate kinetic energy is KE = 0.5mv², where m is the mass of the lamp and v is its velocity. Since the lamp starts from rest, its initial velocity is 0. Using the equation PE = mgh, where m is the mass of the lamp, g is the acceleration due to gravity (9.8 m/s²), and h is the height of the lamp, we can calculate the potential energy.
PE = mgh = 2.9m x 9.8 m/s² = 28.42 m²/s²
Since the potential energy is converted into kinetic energy, we can equate the two expressions:
KE = PE
0.5mv² = mgh
Canceling out the mass:
0.5v² = gh
Substituting the known values:
0.5v² = 9.8 m/s² x 2.9 m
Simplifying the equation:
0.5v² = 28.42 m²/s²
Multiplying both sides by 2:
v² = 56.84 m²/s²
Taking the square root of both sides:
v = 7.54 m/s
Therefore, the impact speed of the lamp is 7.54 m/s.
The impact speed of the lamp falling from a height of 2.9 m is approximately 7.55 m/s. This speed is derived from calculating the potential energy at that height, which converts into kinetic energy just before impact. Using the formula for kinetic energy and the conservation of energy principle allows us to find this speed.
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