Eight bricks 6 cm thick with mass 1.5kg lie flat on a table.how much work is required to top them one on another?
W (for the second brick) = m•g•0.06
W (for the third brick) = m•g•0.12.
W (for the 4th) = m•g•0.18. ....
.................
W(total)=m•g•(0.06+0.12+0.18+ 0.24+0.30+0.36+0.42) =
= 1.68•m•g =1.68•1.5•9.8 =24.7 J
To calculate the work required to stack the bricks one on top of another, we need to determine the total height that the bricks need to be lifted.
Each brick has a thickness of 6 cm, so to stack them, we need to lift each brick by 6 cm. Since we have 8 bricks, the total height to lift is:
Total height = 6 cm x 8 = 48 cm
To convert the height to meters, we divide by 100:
Total height = 48 cm / 100 = 0.48 m
Now, we need to calculate the work required using the formula:
Work = force x distance
The force required to lift a single brick is equal to its weight. The weight of a brick can be calculated by multiplying its mass by the acceleration due to gravity.
Given that the mass of each brick is 1.5 kg and the acceleration due to gravity is 9.8 m/s², the force required to lift each brick is:
Force = mass x acceleration due to gravity
= 1.5 kg x 9.8 m/s²
= 14.7 N
Now, we can calculate the work required to stack all the bricks by multiplying the force by the height:
Work = force x distance
= 14.7 N x 0.48 m
≈ 7.056 J
Therefore, the work required to stack the eight bricks on top of each other is approximately 7.056 Joules.
To calculate the work required to stack the eight bricks one on top of another, we need to consider the gravitational potential energy.
The gravitational potential energy (PE) is given by the formula:
PE = m * g * h,
where m is the mass, g is the acceleration due to gravity, and h is the height. In this case, we need to find the work done to lift each brick (from the table to the top of the stack) and add them up for all eight bricks.
First, let's calculate the height of the stack. Each brick is 6 cm thick, and there are eight bricks. Therefore, the total height (h) of the stack is:
h = 6 cm * 8 = 48 cm = 0.48 m.
The mass of each brick is given as 1.5 kg. So, the work required to lift one brick to the top of the stack is:
Work = PE = m * g * h = 1.5 kg * 9.8 m/s^2 * 0.48 m.
Calculating this, we get:
Work per brick = 7.056 J (Joules).
Finally, to find the total work required to stack all eight bricks, we multiply the work per brick by the number of bricks:
Total work = Work per brick * Number of bricks = (7.056 J) * 8.
Hence, the total work required to stack the eight bricks is:
Total work = 56.448 J (Joules).