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Calculate the k.E. and P.E. of the ball half way up,when a ball of mass 0.1kg is thrown vertically upwards with an initial speed of 20m/s?
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Overview:
To calculate the kinetic energy (KE) and potential energy (PE) of a ball halfway up when thrown vertically upwards, we need to understand the concepts of kinetic and potential energy and apply the relevant formulas.
Explanation:
Kinetic Energy:
- Kinetic energy is the energy possessed by an object due to its motion.
- The formula to calculate kinetic energy is KE = 1/2 * m * v^2, where KE is the kinetic energy, m is the mass of the object, and v is the velocity of the object.
Given data:
- Mass of the ball (m) = 0.1 kg
- Initial velocity (v) = 20 m/s
Let's calculate the kinetic energy of the ball using the given formula:
KE = 1/2 * m * v^2
= 1/2 * 0.1 kg * (20 m/s)^2
= 1/2 * 0.1 kg * 400 m^2/s^2
= 1/2 * 40 kg * m^2/s^2
= 20 kg * m^2/s^2
Therefore, the kinetic energy of the ball halfway up is 20 kg * m^2/s^2.
Potential Energy:
- Potential energy is the energy possessed by an object due to its position or height.
- The formula to calculate potential energy is PE = m * g * h, where PE is the potential energy, m is the mass of the object, g is the acceleration due to gravity, and h is the height of the object.
Given data:
- Mass of the ball (m) = 0.1 kg
- Acceleration due to gravity (g) = 9.8 m/s^2
- Height halfway up (h) = ?
To calculate the height halfway up, we need to consider the projectile motion of the ball. At the highest point, the velocity of the ball becomes zero.
Using the equation of motion:
v^2 = u^2 - 2 * g * h
Where:
v = final velocity (0 m/s at the highest point)
u = initial velocity (20 m/s)
g = acceleration due to gravity (9.8 m/s^2)
h = height halfway up
0^2 = (20 m/s)^2 - 2 * 9.8 m/s^2 * h
0 = 400 m^2/s^2 - 19.6 m/s^2 * h
19.6 m/s^2 * h = 400 m^2/s^2
h = 400 m^2/s^2 / 19.6 m/s^2
h ≈ 20.41 meters
Therefore, the height halfway up is approximately 20.41 meters.
Now, let's calculate the potential energy of the ball using the given formula:
PE = m * g * h
= 0.1 kg * 9.8 m/s^2 * 20.41 meters
= 0.1 kg * 200.218 m^2/s^2
= 20.0218 kg * m^2/s^2
Therefore, the potential energy of the ball halfway up is approximately 20.0218 kg *
To calculate the kinetic energy (KE) and potential energy (PE) of a ball halfway up when thrown vertically upwards, we need to understand the concepts of kinetic and potential energy and apply the relevant formulas.
Explanation:
Kinetic Energy:
- Kinetic energy is the energy possessed by an object due to its motion.
- The formula to calculate kinetic energy is KE = 1/2 * m * v^2, where KE is the kinetic energy, m is the mass of the object, and v is the velocity of the object.
Given data:
- Mass of the ball (m) = 0.1 kg
- Initial velocity (v) = 20 m/s
Let's calculate the kinetic energy of the ball using the given formula:
KE = 1/2 * m * v^2
= 1/2 * 0.1 kg * (20 m/s)^2
= 1/2 * 0.1 kg * 400 m^2/s^2
= 1/2 * 40 kg * m^2/s^2
= 20 kg * m^2/s^2
Therefore, the kinetic energy of the ball halfway up is 20 kg * m^2/s^2.
Potential Energy:
- Potential energy is the energy possessed by an object due to its position or height.
- The formula to calculate potential energy is PE = m * g * h, where PE is the potential energy, m is the mass of the object, g is the acceleration due to gravity, and h is the height of the object.
Given data:
- Mass of the ball (m) = 0.1 kg
- Acceleration due to gravity (g) = 9.8 m/s^2
- Height halfway up (h) = ?
To calculate the height halfway up, we need to consider the projectile motion of the ball. At the highest point, the velocity of the ball becomes zero.
Using the equation of motion:
v^2 = u^2 - 2 * g * h
Where:
v = final velocity (0 m/s at the highest point)
u = initial velocity (20 m/s)
g = acceleration due to gravity (9.8 m/s^2)
h = height halfway up
0^2 = (20 m/s)^2 - 2 * 9.8 m/s^2 * h
0 = 400 m^2/s^2 - 19.6 m/s^2 * h
19.6 m/s^2 * h = 400 m^2/s^2
h = 400 m^2/s^2 / 19.6 m/s^2
h ≈ 20.41 meters
Therefore, the height halfway up is approximately 20.41 meters.
Now, let's calculate the potential energy of the ball using the given formula:
PE = m * g * h
= 0.1 kg * 9.8 m/s^2 * 20.41 meters
= 0.1 kg * 200.218 m^2/s^2
= 20.0218 kg * m^2/s^2
Therefore, the potential energy of the ball halfway up is approximately 20.0218 kg *
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Calculate the k.E. and P.E. of the ball half way up,when a ball of mass 0.1kg is thrown vertically upwards with an initial speed of 20m/s?
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Calculate the k.E. and P.E. of the ball half way up,when a ball of mass 0.1kg is thrown vertically upwards with an initial speed of 20m/s? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about Calculate the k.E. and P.E. of the ball half way up,when a ball of mass 0.1kg is thrown vertically upwards with an initial speed of 20m/s? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Calculate the k.E. and P.E. of the ball half way up,when a ball of mass 0.1kg is thrown vertically upwards with an initial speed of 20m/s?.
Calculate the k.E. and P.E. of the ball half way up,when a ball of mass 0.1kg is thrown vertically upwards with an initial speed of 20m/s? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about Calculate the k.E. and P.E. of the ball half way up,when a ball of mass 0.1kg is thrown vertically upwards with an initial speed of 20m/s? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Calculate the k.E. and P.E. of the ball half way up,when a ball of mass 0.1kg is thrown vertically upwards with an initial speed of 20m/s?.
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