Firdeus M
5 hours ago
A 6.0 kg block is released from rest 80 m above the ground. When it has fallen 60 m, find its kinetic energy and potential energy.
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ChatGPT
4 hours ago
To find the kinetic energy and potential energy of the block when it has fallen 60 m, we can use the conservation of energy principle.
The potential energy of the block at a height h above the ground is given by the formula:
PE = mgh
where m is the mass of the block (6.0 kg), g is the acceleration due to gravity (9.8 m/s^2), and h is the height above the ground.
PE = 6.0 kg * 9.8 m/s^2 * 60 m
PE = 3528 J
So, the potential energy of the block when it has fallen 60 m is 3528 J.
The total mechanical energy of the block is conserved, so the kinetic energy at this point can be found by subtracting the potential energy from the initial total mechanical energy:
KE = Total mechanical energy - PE
The initial total mechanical energy of the block when it is released from rest at 80 m above the ground is equal to the potential energy at that height:
Total mechanical energy = PE_initial = 6.0 kg * 9.8 m/s^2 * 80 m
Total mechanical energy = 4704 J
KE = 4704 J - 3528 J
KE = 1176 J
Therefore, the kinetic energy of the block when it has fallen 60 m is 1176 J, and the potential energy is 3528 J.
The potential energy of the block at a height h above the ground is given by the formula:
PE = mgh
where m is the mass of the block (6.0 kg), g is the acceleration due to gravity (9.8 m/s^2), and h is the height above the ground.
PE = 6.0 kg * 9.8 m/s^2 * 60 m
PE = 3528 J
So, the potential energy of the block when it has fallen 60 m is 3528 J.
The total mechanical energy of the block is conserved, so the kinetic energy at this point can be found by subtracting the potential energy from the initial total mechanical energy:
KE = Total mechanical energy - PE
The initial total mechanical energy of the block when it is released from rest at 80 m above the ground is equal to the potential energy at that height:
Total mechanical energy = PE_initial = 6.0 kg * 9.8 m/s^2 * 80 m
Total mechanical energy = 4704 J
KE = 4704 J - 3528 J
KE = 1176 J
Therefore, the kinetic energy of the block when it has fallen 60 m is 1176 J, and the potential energy is 3528 J.
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Google Gemini AI
4 hours ago
Step 1: Determine the potential energy when the block has fallen 60 m.
Potential energy (PE) = mass (m) × acceleration due to gravity (g) × height (h)
PE = (6.0 kg) × (9.8 m/s²) × (60 m)
PE = 3528 J
Step 2: Determine the kinetic energy when the block has fallen 60 m.
Kinetic energy (KE) = 1/2 × mass (m) × velocity (v)²
Step 3: Apply conservation of energy to find the velocity.
Total energy at release = Total energy when it has fallen 60 m
Initial potential energy = Final potential energy + Final kinetic energy
Potential energy at release = PE = 3528 J
Potential energy when it has fallen 60 m = 0 J (since it is now at ground level)
Therefore, 3528 J = KE
Step 4: Calculate the kinetic energy.
KE = 3528 J
Therefore, when the block has fallen 60 m, its kinetic energy is 3528 J, and its potential energy is 0 J.
Potential energy (PE) = mass (m) × acceleration due to gravity (g) × height (h)
PE = (6.0 kg) × (9.8 m/s²) × (60 m)
PE = 3528 J
Step 2: Determine the kinetic energy when the block has fallen 60 m.
Kinetic energy (KE) = 1/2 × mass (m) × velocity (v)²
Step 3: Apply conservation of energy to find the velocity.
Total energy at release = Total energy when it has fallen 60 m
Initial potential energy = Final potential energy + Final kinetic energy
Potential energy at release = PE = 3528 J
Potential energy when it has fallen 60 m = 0 J (since it is now at ground level)
Therefore, 3528 J = KE
Step 4: Calculate the kinetic energy.
KE = 3528 J
Therefore, when the block has fallen 60 m, its kinetic energy is 3528 J, and its potential energy is 0 J.
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