Energy Loss & Height of Thrown Ball & Marble Fired from Cannon

In summary, the conversation discusses two problems. The first one involves a ball being thrown straight up with a given mass and initial speed, and the question asks for the energy loss due to air resistance, the maximum height the ball would reach without air resistance, and the height it would reach on the moon. The second problem involves a game where two children try to hit a box with a marble fired from a spring-loaded cannon, and the question asks for the distance the spring should be compressed for a successful hit.
  • #1
Kuro
2
0
1. A ball with a mass of 0.5 kg is thrown straight up with an initial speed of 20 m/s. The ball reaches a maximum height of 15 m. (a) Give the energy loss due to air resistance. (b) What height would the ball have reached without air resistance? (c) What height would the ball have reached on the moon (where gravity is only 0.17 that of earth)?

2. Two children are playing a game in which they try to hit a small box on the floor with a marble fired horizontally from a spring-loaded cannon that is mounted on a table. The target box is 2.40 m from the edge of the table. Alex compresses the spring 1.10 cm, but the marble falls 36 cm short. How far should Ben compress the spring to score a hit?
 
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  • #2
Welcome to PF.

How would you think to approach either of these problems?
 
  • #3
In the first problem, I think that the energy loss is between the 1/2mv^2 - mgh?
 
  • #4
Kuro said:
In the first problem, I think that the energy loss is between the 1/2mv^2 - mgh?

Not exactly, if you're looking for air resistance, though certainly that's the energy exchange in throwing a ball in the air.

Maybe consider how high it would go without any resistance using the relationship you suggested?
 

Related to Energy Loss & Height of Thrown Ball & Marble Fired from Cannon

1. How does the height from which a ball or marble is thrown affect its energy loss?

The height from which a ball or marble is thrown does not directly affect its energy loss. However, a higher initial height may result in a longer distance traveled by the object, which can lead to increased air resistance and therefore more energy loss.

2. Does the mass of the ball or marble affect its energy loss?

Yes, the mass of the object does play a role in its energy loss. Objects with greater mass have more inertia and require more energy to move, resulting in a higher energy loss when thrown or fired from a cannon.

3. How does air resistance affect the energy loss of a thrown or fired object?

Air resistance, also known as drag, is a force that opposes the motion of an object through the air. As an object moves through the air, it must push aside air molecules, which requires energy. This energy is then lost from the object, resulting in a decrease in its kinetic energy and therefore a higher energy loss.

4. Is there a difference in energy loss between a ball thrown by hand and a marble fired from a cannon?

Yes, there is a difference in energy loss between a ball thrown by hand and a marble fired from a cannon. The marble fired from a cannon experiences a greater initial velocity, which leads to a higher energy loss due to increased air resistance and friction.

5. Can the energy loss of a thrown or fired object be calculated?

Yes, the energy loss of a thrown or fired object can be calculated using the principles of energy conservation and the equations for kinetic and potential energy. However, the calculation may be affected by factors such as air resistance and the elasticity of the object.

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