1.A 4kg ball moving at 8ms-1 collides with a stationary ball of mass 12kg,and they stick together.calculate the final velocity and kinetic energy lost in the impact.
2.when a person fires a rifle it is advisable to hold the butt firmly against the shoulder rather than a little way from it to minimise the impact on the shoulder.explain why?
Given:
M1 = 4 kg, V1 = 8 m/s.
M2 = 12 kg, V2 = 0.
V3 = velocity of M1 and M2 after the collision.
1. Momentum before = Momentum after.
M1*V1 + M2*V2 = M1*V3 + M2*V3.
4*8 + 12*0 = 4*V3 + 12*V3,
V3 = 2 m/s.
KE before the collision:
0.5M1*V1^2 + 0.5M2*V2^2 = 2*8^2 + 6*0^2 = 128 + 0 = 128 Joules.
KE after the collision:
0.5M1*V3^2 + 0.5M2*V3^2 = 2*2^2 + 6*2^2 = 8 + 24 = 32 Joules.
KE Lost = 128-32 =
1. Well, let's get this collision party started! To calculate the final velocity, we can use the principle of conservation of momentum. The initial momentum of the system is the mass of the first ball (4kg) times its velocity (8m/s), plus the momentum of the second ball (12kg) which is initially at rest (0m/s). That gives us a total initial momentum of 32 kg m/s.
Now, since the two balls stick together after the collision, their masses combine to form a total mass of 4kg + 12kg = 16kg. To find the final velocity, we divide the initial momentum by the total mass. So, 32 kg m/s ÷ 16kg equals a final velocity of 2m/s. Ta-da!
To calculate the kinetic energy lost in the impact, we can look at the initial and final kinetic energy of the system. The initial kinetic energy is given by (½ × mass × velocity^2), which for the first ball is (½ × 4kg × 8m/s^2) = 128J. After the collision, the final kinetic energy is (½ × 16kg × 2m/s^2) = 32J. Therefore, the kinetic energy lost in the impact is simply the difference between these two values, which is 128J - 32J = 96J. It's like a disappearing act for energy!
2. Ah, the joy of physics and rifle etiquette! When a person fires a rifle, it's advisable to hold the butt firmly against the shoulder rather than a little way from it. Why, you may ask? Well, it's all about minimizing the impact on the shoulder, and trust me, your shoulder will thank you for it.
When the rifle is fired, a bullet is propelled forward with a great amount of force. According to Newton's third law of motion, every action has an equal and opposite reaction. So, when the bullet is pushed forward, an equal force is exerted on the rifle in the opposite direction.
By holding the butt firmly against the shoulder, the force from the rifle has a larger area over which to act. This distributes the force more evenly and reduces the pressure on any single point of contact. On the other hand, if the butt is held away from the shoulder, the force is concentrated on a smaller area, which can lead to a more intense impact and a potential shoulder bash party.
So, remember, it's all about giving your shoulder a nice, wide, and soft cushion with the butt of the rifle. Your shoulder will thank you, and who knows, you might even end up with fewer bruised egos... I mean, shoulders.
1. To calculate the final velocity, we can use the principle of conservation of momentum.
The initial momentum before collision can be calculated as follows:
Initial momentum of the 4 kg ball = (mass of the 4 kg ball) x (velocity of the 4 kg ball)
= 4 kg x 8 m/s
= 32 kg m/s
The initial momentum of the 12 kg ball (which is stationary) would be 0 kg m/s.
Since momentum is conserved in the collision, the total momentum after the collision would be equal to the initial momentum.
Total momentum after collision = 32 kg m/s (same as the initial momentum)
Let the final velocity of the combined balls be 'v' m/s.
The final momentum after collision can be calculated as follows:
Final momentum = (combined mass) x (final velocity)
= (4 kg + 12 kg) x v
= 16 kg x v
Now we can equate the final momentum to the initial momentum to find the value of 'v':
16 kg x v = 32 kg m/s
v = 2 m/s
Therefore, the final velocity of the combined balls would be 2 m/s.
To calculate the kinetic energy lost, we need to find the initial kinetic energy and the final kinetic energy.
The initial kinetic energy before collision can be calculated as follows:
Initial kinetic energy of the 4 kg ball = 0.5 x (mass of the 4 kg ball) x (velocity of the 4 kg ball)^2
= 0.5 x 4 kg x (8 m/s)^2
= 128 J
The initial kinetic energy of the 12 kg ball (which is stationary) would be 0 J.
The final kinetic energy after collision can be calculated as follows:
Final kinetic energy = 0.5 x (combined mass) x (final velocity)^2
= 0.5 x (4 kg + 12 kg) x (2 m/s)^2
= 24 J
The kinetic energy lost in the impact can be calculated as the difference between the initial and final kinetic energy:
Kinetic energy lost = Initial kinetic energy - Final kinetic energy
= 128 J - 24 J
= 104 J
Therefore, the kinetic energy lost in the impact is 104 Joules.
2. Holding the butt of the rifle firmly against the shoulder is advisable to minimize the impact on the shoulder because it helps to distribute the recoil force over a larger area.
When a rifle is fired, the gunpowder in the bullet ignites, rapidly increasing the pressure in the barrel and propelling the bullet forward. According to Newton's third law of motion, for every action, there is an equal and opposite reaction. As a result, when the bullet is propelled forward, the rifle experiences a backward force, known as recoil.
By holding the butt firmly against the shoulder, the recoil force is spread over a larger surface area, which helps to distribute the force more evenly and reduce the pressure applied to a smaller area of the shoulder. This reduces the chance of injury or discomfort from the impact force. Holding the rifle away from the shoulder would concentrate the recoil force on a smaller area, increasing the impact and potentially causing more pain or injury.
To calculate the final velocity and kinetic energy lost in the collision of the balls, we can use the principle of conservation of momentum. The law of conservation of momentum states that the total momentum before the collision is equal to the total momentum after the collision, assuming no external forces are acting on the system.
1. Calculation of Final Velocity:
Let the final velocity of the two balls sticking together be Vf. Using the conservation of momentum, we can write the equation as follows:
(m1 * v1) + (m2 * v2) = (m1 + m2) * Vf
Here, m1 and v1 represent the mass and velocity of the 4kg ball (first ball) respectively, and m2 is the mass of the 12kg ball (second ball). The second ball is stationary, so its initial velocity v2 is 0.
Plugging in the values, we get:
(4kg * 8m/s) + (12kg * 0m/s) = (4kg + 12kg) * Vf
32kg·m/s = 16kg * Vf
32kg·m/s = 16kg * Vf
2m/s = Vf
Therefore, the final velocity of the combined balls is 2m/s.
2. Calculation of Kinetic Energy Lost:
To calculate the kinetic energy lost in the impact, we need to find the initial kinetic energy before the collision and the final kinetic energy after the collision. The kinetic energy can be calculated using the formula:
Kinetic Energy = 0.5 * mass * velocity^2
The initial kinetic energy of the system is given by:
KE1 = 0.5 * (4kg) * (8m/s)^2
KE1 = 0.5 * 4kg * 64m^2/s^2
KE1 = 128 Joules
The final kinetic energy of the system after the collision is given by:
KE2 = 0.5 * (4kg + 12kg) * (2m/s)^2
KE2 = 0.5 * 16kg * 4m^2/s^2
KE2 = 32 Joules
The kinetic energy lost in the impact is the difference between the initial and final kinetic energies:
Kinetic Energy Lost = KE1 - KE2
Kinetic Energy Lost = 128 Joules - 32 Joules
Kinetic Energy Lost = 96 Joules
Therefore, the kinetic energy lost in the impact is 96 Joules.
2. When a person fires a rifle, it is advisable to hold the butt firmly against the shoulder rather than a little way from it to minimize the impact on the shoulder. The reason behind this is that holding the butt firmly against the shoulder allows for better distribution of the force generated by the recoil of the rifle.
When a bullet is fired, a high amount of energy is released, propelling the bullet forward. However, according to Newton's third law of motion, for every action, there is an equal and opposite reaction. In this case, the action is the bullet being propelled forward, and the reaction is the recoil force pushing backward.
By firmly holding the butt against the shoulder, the person's body acts as a solid support for absorbing and distributing the backward force of the recoil. This reduces the impact on the shoulder, as the force is spread over a larger area of contact.
If the butt of the rifle is held a little way from the shoulder, the force of the recoil would not be distributed evenly, resulting in a concentrated impact on a smaller area of the shoulder. This can lead to discomfort, bruising, or even injury due to the high force exerted on a small contact area.
In summary, holding the butt firmly against the shoulder while firing a rifle helps to distribute and absorb the recoil force, minimizing the impact on the shoulder and reducing the chances of injury.