Using The Principle Of Momentum Conservation Explainer

Using The Principle Of Momentum Conservation Explain What Happens W

1. Using the principle of momentum conservation, when a moving billiard ball collides with a stationary ball (such as a cue ball hitting the eight ball), the total momentum of the system before the collision equals the total momentum after the collision. If the cue ball possesses momentum due to its velocity, and the eight ball is initially at rest, the collision results in the transfer of momentum from the moving cue ball to the stationary eight ball. Consequently, the cue ball slows down or stops, and the eight ball gains velocity and starts moving in the direction of the initial cue ball. The actual transfer of momentum depends on factors such as the masses of the balls and the nature of the collision (elastic or inelastic), but the overall principle remains: the total momentum before and after the impact remains constant.

2. Energy and power are related but distinct concepts. Energy refers to the capacity to do work and is measured in joules (J); it can exist in various forms such as kinetic energy, potential energy, thermal energy, etc. For example, a stretched bow stores elastic potential energy, while a moving car possesses kinetic energy. Power, on the other hand, is the rate at which work is done or energy is transferred over time and is measured in watts (W), where 1 watt equals 1 joule per second. For instance, lifting a box with a certain amount of energy takes different amounts of power depending on how quickly you perform the lift. Work is the process of energy transfer when a force causes displacement; thus, energy quantifies the quantity of work done, while power measures how quickly that work happens.

3. Considering a 1000-kilogram car lifted to different heights:

• a) The potential energy (PE) with respect to the floor when the car is lifted 1 meter can be calculated using the formula PE = mgh, where m is the mass (1000 kg), g is the acceleration due to gravity (approximately 9.8 m/s²), and h is the height (1 meter). Therefore, PE = 1000 × 9.8 × 1 = 9,800 joules.
• b) If the car is lifted to 2 meters, the potential energy becomes PE = 1000 × 9.8 × 2 = 19,600 joules. This shows that the potential energy doubles when the height doubles, illustrating the linear relationship between potential energy and height.
• c) Potential energy varies linearly with height because PE = mgh; all other factors being constant, as height (h) increases, PE increases proportionally. Graphically, this is a straight line, demonstrating a direct proportionality between the object’s position relative to a reference point (floor) and its stored energy.

4. When catching a fast-moving baseball, it is practical to move your hand in the direction of the ball's motion because doing so increases the time over which the ball's momentum is brought to zero (i.e., stops). According to the work-energy principle, changing the ball’s momentum requires applying a force over a period of time, or equivalently, doing work. Moving your hand in the same direction as the ball allows you to gradually decrease its velocity, reducing the force necessary to stop it and minimizing the impact force. This absorption of the ball’s kinetic energy over a longer time helps prevent injury and reduces the risk of dropping or damaging the ball.

5. To estimate how high a sprinter could jump if all his kinetic energy is converted into potential energy, we apply the energy conservation principle: KE = PE. Kinetic energy is given by KE = (1/2)mv², and potential energy is PE = mgh. Assuming the mass m remains constant and that all kinetic energy is transferred into potential energy, then:

(1/2)mv² = mgh

Dividing through by m, we get:

(1/2)v² = gh

Solving for height h:

h = v² / (2g)

Using v = 10 m/s and g = 9.8 m/s²:

h = (10)² / (2 × 9.8) = 100 / 19.6 ≈ 5.10 meters

Therefore, the sprinter could theoretically jump approximately 5.1 meters high if all kinetic energy were converted into upward potential energy, although in reality, energy conversions are imperfect due to energy losses.

6. During the process of shooting an arrow from a bow, several forms of energy are present. Initially, the archer's muscular effort stores chemical energy in the muscles and chemical bonds of the bowstring material. When the bowstring is drawn, this chemical energy converts into elastic potential energy stored in the tense bow. Upon releasing the string, the elastic potential energy transforms into kinetic energy, propelling the arrow forward. As the arrow moves through the air, it possesses kinetic energy, and air resistance causes some of that energy to dissipate as thermal energy due to air friction. If the arrow hits a target, some kinetic energy is transferred to the target as work, and some may convert into sound and slight deformation energy at the point of impact.

7. Regarding the work and power involved in pushing a lawn mower across a yard:

• a) If you push the lawn mower across the yard in 10 seconds versus in 20 seconds, the total work done in both cases remains essentially the same, assuming the force exerted remains constant and frictional forces are unchanged. Work is calculated as W = force × displacement; thus, the same force over the same distance yields equal work regardless of the time taken.
• c) Power, defined as work done divided by the time taken to do that work, is greater when pushing takes 10 seconds compared to 20 seconds. Since the work done is the same, a shorter duration (10 seconds) means higher average power (P = W / t), as the energy transfer occurs more rapidly in less time. Conversely, slower pushing over 20 seconds results in lower average power output.

References

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