1. Calculate the kinetic energy of a 5.2kg object moving at 2.4 m/s
7. Calculate the potential energy of a 5.2kg object positioned 5.8m above the ground
21. Calculate the speed of a 5.2 kg object that possesses 26.1 J of kinetic energy.
recall that
KE = 1/2 mv^2
PE = mgh
Now just plug in your numbers.
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1. To calculate the kinetic energy of an object, you can use the formula: KE = 0.5 * mass * velocity^2.
Plugging in the values:
Mass = 5.2 kg
Velocity = 2.4 m/s
KE = 0.5 * 5.2 kg * (2.4 m/s)^2
KE = 0.5 * 5.2 kg * 5.76 m^2/s^2
KE = 14.976 J
Therefore, the kinetic energy of the object is 14.976 J.
7. To calculate the potential energy of an object, you can use the formula: PE = mass * gravitational acceleration * height.
Gravitational acceleration is approximately 9.8 m/s^2.
Plugging in the values:
Mass = 5.2 kg
Height = 5.8 m
PE = 5.2 kg * 9.8 m/s^2 * 5.8 m
PE = 302.224 J
Therefore, the potential energy of the object is 302.224 J.
21. To calculate the speed of an object with a given kinetic energy, you can rearrange the formula for kinetic energy and solve for velocity.
KE = 0.5 * mass * velocity^2
Plugging in the values:
Kinetic Energy = 26.1 J
Mass = 5.2 kg
26.1 J = 0.5 * 5.2 kg * velocity^2
52.2 J / 5.2 kg = velocity^2
10 m^2/s^2 = velocity^2
Taking the square root of both sides:
velocity = √(10 m^2/s^2)
velocity ≈ 3.16 m/s
Therefore, the speed of the object is approximately 3.16 m/s.
To calculate the kinetic energy, potential energy, and speed of an object, you can use the respective formulas and substitute the given values into them.
1. Calculate the kinetic energy (KE) of a 5.2kg object moving at 2.4 m/s:
The formula for kinetic energy is KE = 0.5 * mass * velocity^2
Substituting the given values:
KE = (0.5) * 5.2 kg * (2.4 m/s)^2
KE = 0.5 * 5.2 kg * 5.76 m^2/s^2
KE = 14.976 J
Therefore, the kinetic energy of the object is 14.976 J.
7. Calculate the potential energy (PE) of a 5.2kg object positioned 5.8m above the ground:
The formula for potential energy is PE = mass * acceleration due to gravity * height
Substituting the given values:
PE = 5.2 kg * 9.8 m/s^2 * 5.8 m
PE = 301.144 J
Therefore, the potential energy of the object is 301.144 J.
21. Calculate the speed of a 5.2 kg object that possesses 26.1 J of kinetic energy:
Rearranging the formula for kinetic energy:
KE = 0.5 * mass * velocity^2
26.1 J = 0.5 * 5.2 kg * velocity^2
Dividing both sides of the equation by (0.5 * 5.2 kg):
velocity^2 = 26.1 J / (0.5 * 5.2 kg)
velocity^2 = 10 J/kg
Taking the square root of both sides:
velocity = √(10 J/kg)
velocity ≈ 3.162 m/s (approx.)
Therefore, the speed of the object is approximately 3.162 m/s.