We appreciate your visit to According to the label on a soft drink one serving provides 185 kcal If all of this energy is used to lift 1 0 kg. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!
Answer :
The number of blocks that can be lifted through this height is 11563 blocks.
How many blocks can be lifted?
We know that we define the term energy as the ability to do work, Now we have to consider the fact that we are told that one serving provides 185 kcal. Then we are told that all of this energy is used to lift 1.0-kg blocks through a distance of 7.0 meters.
Given that the energy exerted in lifting each block is;
mgh
m = mass of the block
g = acceleration due to gravity
h = height lifted through
E = 1.0-kg * 9.8 m/s^2 * 7.0 meters = 68.6 J or 0.016 kcal
The number of blocks that can be lifted = 185 kcal/ 0.016 kcal
= 11563 blocks
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Rewritten by : Barada
The energy from one serving of the soft drink can lift approximately [tex]11,271 1.0\ kg[/tex] blocks a distance of [tex]7.0 \ meters.[/tex]
Use the formula for gravitational potential energy to find out how many blocks can be lifted.
1. Convert energy from kilocalories to joules:
[tex]\[ 1 \, \text{kcal} = 4,184 \, \text{J} \][/tex]
So, the energy in joules is:
[tex]\[ 185 \, \text{kcal} \times 4,184 \, \text{J/kcal} = 773,240 \, \text{J} \][/tex]
2. Calculate the energy required to lift one [tex]1.0\ kg[/tex] block [tex]7.0 \ meters[/tex]
The gravitational potential energy [tex](\(E\))[/tex] required to lift an object is given by the formula:
[tex]\[ E = mgh \][/tex]
Where:
[tex]\( m \)[/tex] is the mass ([tex]1.0 \ kg[/tex])
[tex]\( g \)[/tex] is the acceleration due to gravity ([tex]9.8\ m/s^2[/tex])
[tex]\( h \)[/tex] is the height ([tex]7.0 \ meters[/tex])
[tex]\[ E = 1.0 \, \text{kg} \times 9.8 \, \text{m/s}^2 \times 7.0 \, \text{m} = 68.6 \, \text{J} \][/tex]
3. Determine how many blocks can be lifted:
Now, we divide the total available energy by the energy required to lift one block:
[tex]\[ \text{Number of blocks} = \frac{773,240 \, \text{J}}{68.6 \, \text{J/block}} \][/tex]
[tex]\[ \text{Number of blocks} = 11,271 \][/tex]
