4.80-kg watermelon is dropped (zero initial speed) from the roof of a 25.0-m-tall building. a) Calculate the work done by gravity on the watermelon during its displacement from the roof to the ground. b) What is the kinetic energy of the watermelon just before it strikes the ground? You can ignore air resistance.
Work is force times distance
Force is mass times acceleration
Your acceleration is g=9.8 m/s, mass is 4.8 kg
So force is 9.8*4.8= 47 kg m/s, and distance is 25m
(a) Work then becomes 25*47=1176 J
Kinetic energy is the same as work, since you don't have any air resistance. KE=1176J
To solve this problem, we can use the concepts of work done and gravitational potential energy.
a) The work done by gravity on the watermelon during its displacement can be calculated using the formula:
Work = Force x Distance x cos(theta)
In this case, the force acting on the watermelon is the weight of the watermelon (mg), and the distance is the height of the building (25.0 m).
So, the work done by gravity on the watermelon is:
Work = weight x distance x cos(theta)
= mg x d x cos(theta)
= (4.80 kg) x (9.8 m/s^2) x (25.0 m) x cos(180°)
= (-1176 J)
Since the watermelon falls vertically down, the angle between the force and the displacement is 180°, and the cosine of 180° is -1.
Therefore, the work done by gravity on the watermelon during its displacement from the roof to the ground is -1176 Joules.
b) The kinetic energy of the watermelon just before it strikes the ground can be calculated using the principle of conservation of energy.
The initial potential energy of the watermelon when it is dropped from the roof is given by:
Potential Energy = mgh
Where m is the mass of the watermelon, g is the acceleration due to gravity, and h is the height of the building.
Potential Energy = (4.80 kg) x (9.8 m/s^2) x (25.0 m)
= 1176 Joules
By the principle of conservation of energy, this potential energy is converted entirely into kinetic energy just before it strikes the ground.
So, the kinetic energy of the watermelon just before it strikes the ground is 1176 Joules.
To find the work done by gravity on the watermelon, we can use the formula:
Work = Force x Distance x cos(θ)
In this case, the force is the gravitational force acting on the watermelon, the distance is the height of the building, and θ is the angle between the force and the direction of displacement (which is 0 degrees, since the force is acting vertically downwards).
a) Calculation of work done by gravity:
Weight (force due to gravity) = mass x acceleration due to gravity
Weight = 4.80 kg x 9.8 m/s^2
Weight = 47.04 N (downwards)
Work = Force x Distance x cos(θ)
Work = Weight x distance x cos(0)
Work = 47.04 N x 25.0 m x cos(0)
Work = 1176 J
Therefore, the work done by gravity on the watermelon during its displacement from the roof to the ground is 1176 Joules.
b) To find the kinetic energy of the watermelon just before it strikes the ground, we can use the principle of conservation of energy.
The total mechanical energy of the watermelon is conserved, which is the sum of its potential energy (PE) and kinetic energy (KE).
At the roof of the building, the watermelon has only potential energy, given by:
PE = mgh
PE = 4.80 kg x 9.8 m/s^2 x 25.0 m
PE = 1176 J
As the watermelon falls to the ground, it loses potential energy and gains an equal amount of kinetic energy, assuming no energy losses due to air resistance.
Therefore, at the ground level, the kinetic energy of the watermelon is equal to the potential energy it had initially:
KE = PE = 1176 J
Hence, the kinetic energy of the watermelon just before it strikes the ground is 1176 Joules.