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Sagot :
Of course! Let's break down and solve each part of the problem step-by-step:
### Part 1: Kinetic Energy of the Volleyball
1. We are given the mass of the volleyball: [tex]\( m = 1.7 \)[/tex] kg.
2. We are also given the speed of the volleyball: [tex]\( v = 27 \)[/tex] m/s.
The formula for kinetic energy [tex]\( KE \)[/tex] is:
[tex]\[ KE = \frac{1}{2} m v^2 \][/tex]
Substitute the given values into the formula:
[tex]\[ KE = \frac{1}{2} \times 1.7 \times (27)^2 \][/tex]
When you calculate this, you get:
[tex]\[ KE = 0.5 \times 1.7 \times 729 \][/tex]
[tex]\[ KE = 0.85 \times 729 \][/tex]
[tex]\[ KE = 619.65 \][/tex]
So, the kinetic energy of the volleyball is 619.65 Joules.
### Part 2: Potential Energy of the Cinder Block
1. We are given the mass of the cinder block: [tex]\( m = 8.06 \)[/tex] kg.
2. The height at which the cinder block is located: [tex]\( h = 18 \)[/tex] m.
3. The acceleration due to gravity [tex]\( g \)[/tex] is [tex]\( 9.81 \)[/tex] m/s[tex]\(^2\)[/tex].
The formula for potential energy [tex]\( PE \)[/tex] is:
[tex]\[ PE = m g h \][/tex]
Substitute the given values into the formula:
[tex]\[ PE = 8.06 \times 9.81 \times 18 \][/tex]
When you calculate this, you get:
[tex]\[ PE = 8.06 \times 9.81 \times 18 \][/tex]
[tex]\[ PE = 1423.2348 \][/tex]
So, the potential energy of the cinder block is 1423.2348 Joules.
### Part 3: Height of the Bell
1. We are given the potential energy of the bell: [tex]\( PE = 3802 \)[/tex] Joules.
2. The mass of the bell: [tex]\( m = 19.4 \)[/tex] kg.
3. The acceleration due to gravity [tex]\( g \)[/tex] is [tex]\( 9.81 \)[/tex] m/s[tex]\(^2\)[/tex].
We need to find the height [tex]\( h \)[/tex]. The formula for height derived from the potential energy formula is:
[tex]\[ h = \frac{PE}{mg} \][/tex]
Substitute the given values into the formula:
[tex]\[ h = \frac{3802}{19.4 \times 9.81} \][/tex]
When you calculate this, you get:
[tex]\[ h = \frac{3802}{190.314} \][/tex]
[tex]\[ h = 19.977510850489193 \][/tex]
So, the height at which the bell is located is 19.977510850489193 meters.
Thus, we have calculated the following results:
1. The kinetic energy of the volleyball is 619.65 Joules.
2. The potential energy of the cinder block is 1423.2348 Joules.
3. The height of the bell is approximately 19.98 meters.
I hope this answer helps! Please let me know if you need further assistance.
### Part 1: Kinetic Energy of the Volleyball
1. We are given the mass of the volleyball: [tex]\( m = 1.7 \)[/tex] kg.
2. We are also given the speed of the volleyball: [tex]\( v = 27 \)[/tex] m/s.
The formula for kinetic energy [tex]\( KE \)[/tex] is:
[tex]\[ KE = \frac{1}{2} m v^2 \][/tex]
Substitute the given values into the formula:
[tex]\[ KE = \frac{1}{2} \times 1.7 \times (27)^2 \][/tex]
When you calculate this, you get:
[tex]\[ KE = 0.5 \times 1.7 \times 729 \][/tex]
[tex]\[ KE = 0.85 \times 729 \][/tex]
[tex]\[ KE = 619.65 \][/tex]
So, the kinetic energy of the volleyball is 619.65 Joules.
### Part 2: Potential Energy of the Cinder Block
1. We are given the mass of the cinder block: [tex]\( m = 8.06 \)[/tex] kg.
2. The height at which the cinder block is located: [tex]\( h = 18 \)[/tex] m.
3. The acceleration due to gravity [tex]\( g \)[/tex] is [tex]\( 9.81 \)[/tex] m/s[tex]\(^2\)[/tex].
The formula for potential energy [tex]\( PE \)[/tex] is:
[tex]\[ PE = m g h \][/tex]
Substitute the given values into the formula:
[tex]\[ PE = 8.06 \times 9.81 \times 18 \][/tex]
When you calculate this, you get:
[tex]\[ PE = 8.06 \times 9.81 \times 18 \][/tex]
[tex]\[ PE = 1423.2348 \][/tex]
So, the potential energy of the cinder block is 1423.2348 Joules.
### Part 3: Height of the Bell
1. We are given the potential energy of the bell: [tex]\( PE = 3802 \)[/tex] Joules.
2. The mass of the bell: [tex]\( m = 19.4 \)[/tex] kg.
3. The acceleration due to gravity [tex]\( g \)[/tex] is [tex]\( 9.81 \)[/tex] m/s[tex]\(^2\)[/tex].
We need to find the height [tex]\( h \)[/tex]. The formula for height derived from the potential energy formula is:
[tex]\[ h = \frac{PE}{mg} \][/tex]
Substitute the given values into the formula:
[tex]\[ h = \frac{3802}{19.4 \times 9.81} \][/tex]
When you calculate this, you get:
[tex]\[ h = \frac{3802}{190.314} \][/tex]
[tex]\[ h = 19.977510850489193 \][/tex]
So, the height at which the bell is located is 19.977510850489193 meters.
Thus, we have calculated the following results:
1. The kinetic energy of the volleyball is 619.65 Joules.
2. The potential energy of the cinder block is 1423.2348 Joules.
3. The height of the bell is approximately 19.98 meters.
I hope this answer helps! Please let me know if you need further assistance.
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