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Activity 3.3 - Introduction to Potential Energy When you lift a ball up and release it, the ball gains kinetic energy as it falls. There is a form of energy associated with height which is converted to kinetic energy as the ball falls. This energy is called the gravitational potential energy. Consider the Earth and the ball as our system. When two objects within the system interact via a conservative force such as gravity, work done against that force can be stored as potential energy, i.e., the change in gravitational potential energy during a process is negative of the work done by gravity AUgrav=-Waray = mg (h, -h₁). From this, the gravitational potential energy is: Ugrav = mgh, where h is the height above an arbitrarily defined h = 0 position. The sum of the kinetic and potential energy is called the mechanical energy of the system Emech = KE+U If no external forces do work and there are no frictional forces, then the mechanical energy will not change: AE = AKE + AU = 0 That is, any change potential energy is opposite the change in kinetic energy so that the sum always stays the same. If this is the case, then we say that the mechanical energy is conserved so that the mechanical energy is the same any two points in the process: KE₁ + U₁ = KE₁ + U₁ 1. Shaquille O'Neal (retired basketball player famous for being bad at free throws) shoots a free throw during a NBA game. He releases the basketball of 0.625 kg with a speed of 6 m/s from a height of 2.5 meters above the floor. The ball travels a horizontal distance of 2 meters when it reaches the peak of its trajectory at 4 meters above the floor. a. What is the kinetic energy of the basketball when it is released? b. Taking the floor as h = 0, what is the gravitational potential energy of the ball when it is released?

Activity 3.3 - Introduction to Potential Energy When you lift a ball up and release it, the ball gains kinetic energy as it falls. There is a form of energy associated with height which is converted to kinetic energy as the ball falls. This energy is called the gravitational potential energy. Consider the Earth and the ball as our system. When two objects within the system interact via a conservative force such as gravity, work done against that force can be stored as potential energy, i.e., the change in gravitational potential energy during a process is negative of the work done by gravity AUgrav=-Waray = mg (h, -h₁). From this, the gravitational potential energy is: Ugrav = mgh, where h is the height above an arbitrarily defined h = 0 position. The sum of the kinetic and potential energy is called the mechanical energy of the system Emech = KE+U If no external forces do work and there are no frictional forces, then the mechanical energy will not change: AE = AKE + AU = 0 That is, any change potential energy is opposite the change in kinetic energy so that the sum always stays the same. If this is the case, then we say that the mechanical energy is conserved so that the mechanical energy is the same any two points in the process: KE₁ + U₁ = KE₁ + U₁ 1. Shaquille O'Neal (retired basketball player famous for being bad at free throws) shoots a free throw during a NBA game. He releases the basketball of 0.625 kg with a speed of 6 m/s from a height of 2.5 meters above the floor. The ball travels a horizontal distance of 2 meters when it reaches the peak of its trajectory at 4 meters above the floor. a. What is the kinetic energy of the basketball when it is released? b. Taking the floor as h = 0, what is the gravitational potential energy of the ball when it is released?

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Activity 3.3 - Introduction to Potential Energy When you lift a ball up and release it, the ball gains kinetic energy as it falls. There is a form of energy associated with height which is converted to kinetic energy as the ball falls. This energy is called the gravitational potential energy. Consider the Earth and the ball as our system. When two objects within the system interact via a conservative force such as gravity, work done against that force can be stored as potential energy, i.e., the change in gravitational potential energy during a process is negative of the work done by gravity AUgrav=-Waray = mg (h, -h₁). From this, the gravitational potential energy is: Ugrav = mgh, where h is the height above an arbitrarily defined h = 0 position. The sum of the kinetic and potential energy is called the mechanical energy of the system Emech = KE+U If no external forces do work and there are no frictional forces, then the mechanical energy will not change: AE = AKE + AU = 0 That is, any change potential energy is opposite the change in kinetic energy so that the sum always stays the same. If this is the case, then we say that the mechanical energy is conserved so that the mechanical energy is the same any two points in the process: KE₁ + U₁ = KE₁ + U₁ 1. Shaquille O'Neal (retired basketball player famous for being bad at free throws) shoots a free throw during a NBA game. He releases the basketball of 0.625 kg with a speed of 6 m/s from a height of 2.5 meters above the floor. The ball travels a horizontal distance of 2 meters when it reaches the peak of its trajectory at 4 meters above the floor. a. What is the kinetic energy of the basketball when it is released? b. Taking the floor as h = 0, what is the gravitational potential energy of the ball when it is released?
Transcribed Image Text:Activity 3.3 - Introduction to Potential Energy When you lift a ball up and release it, the ball gains kinetic energy as it falls. There is a form of energy associated with height which is converted to kinetic energy as the ball falls. This energy is called the gravitational potential energy. Consider the Earth and the ball as our system. When two objects within the system interact via a conservative force such as gravity, work done against that force can be stored as potential energy, i.e., the change in gravitational potential energy during a process is negative of the work done by gravity AUgrav=-Waray = mg (h, -h₁). From this, the gravitational potential energy is: Ugrav = mgh, where h is the height above an arbitrarily defined h = 0 position. The sum of the kinetic and potential energy is called the mechanical energy of the system Emech = KE+U If no external forces do work and there are no frictional forces, then the mechanical energy will not change: AE = AKE + AU = 0 That is, any change potential energy is opposite the change in kinetic energy so that the sum always stays the same. If this is the case, then we say that the mechanical energy is conserved so that the mechanical energy is the same any two points in the process: KE₁ + U₁ = KE₁ + U₁ 1. Shaquille O'Neal (retired basketball player famous for being bad at free throws) shoots a free throw during a NBA game. He releases the basketball of 0.625 kg with a speed of 6 m/s from a height of 2.5 meters above the floor. The ball travels a horizontal distance of 2 meters when it reaches the peak of its trajectory at 4 meters above the floor. a. What is the kinetic energy of the basketball when it is released? b. Taking the floor as h = 0, what is the gravitational potential energy of the ball when it is released?
d. What is the kinetic energy of the ball at the peak of its trajectory? (It is definitely not zero-use conservation of mechanical energy!) e. What is the speed of the ball at the peak of its trajectory? Elastic Potential Energy: The work against the spring force can be stored as elastic potential energy and that the elastic energy is U₁₁ = x(x − xaq)². Often (but not always), we can choose our coordinate system so x = 0 so that U = kx²/2. 2. The graph shows a plot of the x component of the spring force as a horizontal spring is stretched and compress through its equilibrium position. Recall that the spring force is pr.x = -k(x − xeq)- a. What is the equilibrium length of this spring? (find where the force is zero, this is x in the above equations) b. What is the spring constant? (slope of graph) 10 5 F₂ 0 (N) -5 -10 -15 0.3 0.4 0.5 0.6 0.7 0.8 0.9 spring length (m) c. What is the change in elastic potential energy as this spring, initially compressed to a length of 0.3 meters, is stretched to 0.9 meters? The answer is not 4.5 joules. d. Work done against the spring force can be stored as elastic potential energy. Therefore AE elastic is the negative of the work by the spring force. Use the area "under" the F, vs. x graph to find the work done by the spring force. Check that this is the negative of your answer to c.
Transcribed Image Text:d. What is the kinetic energy of the ball at the peak of its trajectory? (It is definitely not zero-use conservation of mechanical energy!) e. What is the speed of the ball at the peak of its trajectory? Elastic Potential Energy: The work against the spring force can be stored as elastic potential energy and that the elastic energy is U₁₁ = x(x − xaq)². Often (but not always), we can choose our coordinate system so x = 0 so that U = kx²/2. 2. The graph shows a plot of the x component of the spring force as a horizontal spring is stretched and compress through its equilibrium position. Recall that the spring force is pr.x = -k(x − xeq)- a. What is the equilibrium length of this spring? (find where the force is zero, this is x in the above equations) b. What is the spring constant? (slope of graph) 10 5 F₂ 0 (N) -5 -10 -15 0.3 0.4 0.5 0.6 0.7 0.8 0.9 spring length (m) c. What is the change in elastic potential energy as this spring, initially compressed to a length of 0.3 meters, is stretched to 0.9 meters? The answer is not 4.5 joules. d. Work done against the spring force can be stored as elastic potential energy. Therefore AE elastic is the negative of the work by the spring force. Use the area "under" the F, vs. x graph to find the work done by the spring force. Check that this is the negative of your answer to c.
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