A dram of mass 100kg is rolled into the deck of long 1.5m above a horizontally floor using a plank 4m long.calculate the work done against gravity during the process
[Take g=10ms'2]
m g h
100 * 10 * 1.5 =1500 Joules
To calculate the work done against gravity, we need to determine the change in potential energy of the drum.
The potential energy of an object at height h above the ground is given by the equation:
PE = mgh
Where:
PE is the potential energy
m is the mass of the object (100 kg in this case)
g is the acceleration due to gravity (10 m/s^2)
h is the height above the ground (1.5 m in this case)
First, we need to calculate the initial potential energy (PE_initial) of the drum when it is on the deck before being rolled onto the plank.
PE_initial = mgh
PE_initial = 100 kg * 10 m/s^2 * 1.5 m
PE_initial = 1500 joules
Next, we need to calculate the final potential energy (PE_final) of the drum when it reaches the end of the plank.
The drum rolls along a 4 m plank, so the height of the drum when it reaches the end of the plank will be 0 m.
PE_final = mgh
PE_final = 100 kg * 10 m/s^2 * 0 m
PE_final = 0 joules
The work done against gravity is the difference between the initial and final potential energy:
Work done against gravity = PE_final - PE_initial
Work done against gravity = 0 joules - 1500 joules
Work done against gravity = -1500 joules
Therefore, the work done against gravity during the process is -1500 joules.
To calculate the work done against gravity, we need to find the vertical distance through which the dram is lifted.
Given:
Mass of the dram, m = 100 kg
Height of the deck above the floor, h = 1.5 m
Length of the plank, l = 4 m
Acceleration due to gravity, g = 10 m/s^2
Since the dram is rolled into the deck, we can consider the motion as a combination of rolling and translation. The work done against gravity is equal to the potential energy gained by the dram.
The potential energy (PE) is given by the formula:
PE = mgh
Where:
m = mass of the dram
g = acceleration due to gravity
h = height
In this case, the height is the vertical distance through which the dram is lifted. To find this height, we can use the Pythagorean theorem.
Using the Pythagorean theorem, we have:
l^2 = h^2 + d^2
Where:
l = length of the plank
h = height
d = horizontal distance covered by the plank
Rearranging the equation, we get:
h^2 = l^2 - d^2
Substituting the given values:
h^2 = (4m)^2 - (1.5m)^2
h^2 = 16m^2 - 2.25m^2
h^2 = 13.75m^2
h ≈ 3.71m (approximately)
Now, we can substitute the values of m, g, and h into the potential energy equation:
PE = mgh
PE = (100kg)(10m/s^2)(3.71m)
PE ≈ 3710 J
Therefore, the work done against gravity during the process is approximately 3710 Joules.