An electric cannon, such as shown in Figure 14.15, consists...

An electric cannon, such as shown in Figure 14.15, consists of a 10 -kg metal ball with charge $+2.0 \times 10^{-4} \mathrm{C}$ compressed into a plastic barrel so that it is 0.10 $\mathrm{m}$ from an equally charged object at the closed end of the barrel. The barrel is oriented at $37^{\circ}$ with respect to the horizontal. When the ball is released, it shoots 3.0 m along the barrel from its starting position because of the repulsive force between the two charged objects. Determine three physical quantities that describe the motion of the ball after it leaves the barrel.

Key Concepts

Projectile Motion

Projectile motion is the study of objects launched into the air and influenced only by gravity (assuming air resistance is negligible). It involves analyzing the motion through independent horizontal and vertical components; the horizontal component remains constant throughout the flight while the vertical component is uniformly accelerated due to gravity. This concept allows one to determine key quantities such as time of flight, maximum height, and horizontal range.

Work-Energy Principle

The work-energy principle relates the work done on an object by forces to its change in kinetic energy. In scenarios where a force is applied over a distance (for instance, when an object is accelerated in a barrel), the work done by that force is converted into kinetic energy. This principle is used to calculate the initial speed of an object as it leaves a propulsion mechanism, by equating the work input to the kinetic energy achieved.

Vector Decomposition

Vector decomposition involves breaking down a vector into its perpendicular components, usually horizontal and vertical components. When analyzing projectile motion, the initial velocity vector is decomposed to determine the separate contributions in the horizontal direction (which affects range) and in the vertical direction (which affects height and time of flight). This approach simplifies the analysis of motion by allowing separate consideration of the independent kinematics in each direction.

Transcript

00:01 Okay, so the question was asking us to determine three physical quantities that describe the motion of the ball after it leaves the barrel.

00:12 Okay? so, well, let's determine three quantities.

00:21 Well, the first quantity i try trying to determine is the initial potential energy, okay? which is equal to k -tans q1, q2 over r, let's say, r -i, r initial, okay? and we know that both q1 and q2 have same amount of charges and same sign of the charges as well, which is positive 2 .0 times 10 to the power of negative 4 pull loss.

00:42 Therefore, we have initial potential energy is equal to kq squared over our initial.

00:49 And if we plug in the values, we have 9 times 10 to the power of 9, newton times meter square per koulon square times 2 .0 times 2 .0 times 10 to the power of negative 4 koulaum and then holding square over the initial distance which is given as 0 .10 meter okay and this will give us the initial electrical energy is about it's about 3 ,600 jude okay and now let's determine the final electrical energy which is uf okay and this is given it is equal to k k k k1 k2 over r final okay and remember k1 k2 was equal to each other okay and therefore this can be equal to k k k k k u square over r final okay if we plug in the values, we have 9 times 10 to the power of 9 newtown times meter square per kolon square times q square, which is 2 .0 times 10 to the power of negative 4, colon, to the power of square over our final, which should be 3 .0 meter plus 0.

02:49 1 meter.

02:51 Okay? it's because remember in question we're saying that when the ball is released it shoots 3 meter along the barrel from its starting position and the ball's starting position was 0 .1 meter okay because it was saying that it was 0 .1 meter found an equally charged object at a close end of the barrel...

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