In one part of this unit's sample work, we tested how mass impacts kinetic energy. First, the teacher allowed one ball to roll freely down a ramp. Then, from the same height on the ramp, she allowed a ball with greater mass to roll freely down the ramp. Each ball was allowed to strike a cup at the bottom of the ramp.

Question

a. How did mass affect the ability of each ball to move the cup?

Answer 1

In this experiment, mass plays a significant role in determining the kinetic energy of the balls as they strike the cup at the bottom of the ramp. The kinetic energy (KE) of an object is defined by the equation:

\[ KE = \frac{1}{2} mv^2 \]

where \( m \) is the mass of the object and \( v \) is its velocity.

1. Potential Energy at the Top: Both balls start from the same height on the ramp, which means they have the same gravitational potential energy (PE) at the top of the ramp, given by:

\[ PE = mgh \]

where \( g \) is the acceleration due to gravity and \( h \) is the height. Therefore, the initial potential energy is directly proportional to the mass of each ball.

2. Conversion to Kinetic Energy: As each ball rolls down the ramp, its potential energy is converted into kinetic energy. If we assume no energy losses to friction or air resistance, the total energy at the bottom will be the same for both balls—equal to their initial potential energy.

3. Impact on the Cup: When each ball strikes the cup, the force exerted on the cup depends on the kinetic energy of the ball. Since the velocity of both balls will be similar if they are released from the same height, the main difference in their ability to move the cup comes from their mass. The ball with greater mass will have a greater kinetic energy upon impact:

   • The ball with greater mass (m2) will exert more force on the cup when it strikes, due to its larger mass contributing to the kinetic energy (\( KE = \frac{1}{2} m_2 v^2 \)).
   • The ball with lesser mass (m1) will exert less force compared to the heavier ball.

Thus, the ball with greater mass will likely be more effective at moving the cup or causing it to topple over compared to the lighter ball, illustrating that greater mass results in an increased ability to cause movement due to the greater kinetic energy upon impact.

Answer 2

b. How did the mass of the ball impact the ball's kinetic energy?

Answer 3

The mass of the ball directly impacts its kinetic energy, as described by the kinetic energy formula:

\[ KE = \frac{1}{2} mv^2 \]

Where:

• \( KE \) is the kinetic energy,
• \( m \) is the mass of the ball,
• \( v \) is the velocity of the ball.

1. Relationship Between Mass and Kinetic Energy: According to the formula, kinetic energy is directly proportional to the mass of the object. This means that if the velocity (\( v \)) remains constant, an increase in mass (\( m \)) will result in a proportionate increase in kinetic energy. In simpler terms, if you double the mass of the ball while keeping its speed the same, the kinetic energy will also double.

2. Same Height, Different Masses: In the context of your experiment, both balls were released from the same height, resulting in the same initial gravitational potential energy (PE). When each ball rolls down the ramp, this potential energy is converted into kinetic energy as they reach the bottom.

3. Effect on Kinetic Energy at the Bottom: If both balls reached the bottom of the ramp with similar velocities (assuming minimal energy loss), the kinetic energy of each ball can still differ due to their mass:

   • The ball with the greater mass will have a greater kinetic energy when it reaches the bottom of the ramp, simply because it had more mass contributing to the kinetic energy calculation, even if its speed is similar to that of the lighter ball.

4. Conclusion: To summarize, the mass of the ball impacts its kinetic energy significantly. The heavier ball will possess more kinetic energy at the bottom of the ramp when compared to a lighter ball (with comparable velocity), which means it will have a greater ability to do work (such as moving the cup) upon impact. Thus, mass is a crucial factor in determining how much kinetic energy a ball will have as it reaches the end of the ramp.

Answer 4

b. How did the mass of the ball impact the ball's kinetic energy?

A decrease in mass caused an increase in kinetic energy.
An increase in mass caused a decrease in kinetic energy.
Mass did not impact kinetic energy.
An increase in mass caused an increase in kinetic energy.

Answer 5

The correct statement regarding how mass impacts the ball's kinetic energy is:

An increase in mass caused an increase in kinetic energy.

This is because kinetic energy is directly proportional to mass, as represented in the formula:

\[ KE = \frac{1}{2} mv^2 \]

If the velocity of the ball remains constant, an increase in mass will result in an increase in kinetic energy.

Answer 6

c. What happened to the kinetic energy of the ball when it hit the cup?

Answer 7

When the ball hits the cup, several important effects regarding its kinetic energy occur:

1. Transfer of Energy: Upon impact with the cup, the kinetic energy of the ball is transferred to the cup. This transfer may cause the cup to move, topple, or vibrate, depending on the force of the impact and the mass and velocity of the ball.

2. Conversion of Energy: The kinetic energy of the ball is not conserved in the way that it stays as kinetic energy after the collision. Instead, some of the kinetic energy is transformed into other forms of energy, such as:

   • Sound Energy: Some energy may be converted into the sound produced when the ball strikes the cup.
   • Thermal Energy: A portion of the energy may also be transformed into heat due to friction and deformation at the point of impact.
   • Potential Energy of the Cup: If the cup moves or shifts, some of the kinetic energy of the ball is converted into potential energy, elevating the cup slightly if it tips or moves.

3. Dissipation of Energy: In inelastic collisions (which typically occur in this scenario), not all the kinetic energy is retained in the ball-cup system. The energy is dissipated through sound, heat, and movement rather than remaining as kinetic energy in the ball or cup.

4. Post-Impact Kinetic Energy: After the ball hits the cup, its kinetic energy is reduced. The ball will usually come to a stop or slow down significantly, depending on the impact's force and the angle at which it strikes. The cup may gain some kinetic energy if it moves as a result of the impact.

In summary, when the ball hits the cup, its kinetic energy is transferred and transformed, leading to a decrease in the ball's kinetic energy and the potential activation of other forms of energy within the cup and the surrounding environment.