A drum of mass 100kg is rolled into the deck of a lorry 1.5m above a horizontal floor using a plank 4m long. Calculate the work done against gravity during the process(g=10m/s^2)?
I need the solve and the answer
work done=force ×distance
W=FD
F=ma
F=100×10=1000N
d=1.5
w=1000N×1.5
w=1,500j
work done=1,500J
work done=force ×distance
W=FD
F=ma
F=100×10=1000N
d=1.5
w=1000N
=1000N×1.5
=1,500j
Work Done =1,500
Is this correct?
6000joule
Well, to calculate the work done against gravity, we need to find the vertical distance the drum is lifted and multiply it by its weight.
The vertical distance the drum is lifted is equal to the height of the lorry, which is 1.5m. So, we have:
Work = force x distance
The force against gravity, also known as weight, is the mass of the drum multiplied by the acceleration due to gravity:
Weight = mass x acceleration due to gravity
Weight = 100kg x 10m/s^2
Weight = 1000N
Now, we can calculate the work done against gravity:
Work = force x distance
Work = 1000N x 1.5m
Work = 1500J
So, the work done against gravity during the process is 1500 Joules. That's a pretty heavy workout for the drum! Keep it rolling!
To calculate the work done against gravity, we need to find the vertical height the drum is lifted against gravity when it is rolled onto the deck of the lorry.
Using the concept of a lever and assuming the plank is weightless, we can consider the system in equilibrium when the drum is at its highest point on the plank. At this point, the clockwise moment (due to the force against gravity) is balanced by the anticlockwise moment (due to the normal force exerted by the plank).
First, we need to find the distance from the highest point on the plank (where the drum is placed) to the fulcrum (the point where the plank is placed on the lorry's deck). We can use the concept of similar triangles to do this.
Let's call the distance from the fulcrum to the ground on the lorry side x. The length of the plank is given as 4m. So, in the triangle formed by the plank, the lorry deck, and the ground, we have the following relationship:
x / 1.5 = (4 - x) / 4
Simplifying the equation:
4x = 6 - 1.5x
5.5x = 6
x = 6 / 5.5 ≈ 1.09 m
So, the distance from the highest point on the plank to the fulcrum is approximately 1.09 m.
Now, we can calculate the height the drum is lifted against gravity. Since the plank is horizontal and the drum is at its highest point on the plank, the vertical distance it is lifted is equal to the difference in height between the lorry's deck and the ground on the other side.
This height is given as 1.5 m in the problem statement.
So, the work done against gravity can be calculated using the formula:
Work = force × distance × cos(θ)
Since the force against gravity is equal to the weight of the drum, we can calculate the work done as:
Work = mg × h × cos(θ)
where m is the mass of the drum, g is the acceleration due to gravity, h is the height the drum is lifted against gravity, and θ is the angle between the force and the displacement (in this case, 0 degrees since the force is vertical).
Plugging in the values:
Work = 100 kg × 10 m/s^2 × 1.5 m × cos(0°)
Work = 1500 J
Therefore, the work done against gravity during the process is 1500 Joules.