To determine the velocity of a pellet fin a gun.a piece of plasticine of mass 50kg is balanced at the edge of the table such that tlit fails to falloff .a pellet of mass 10g is fired horizontally into the plasticine and remains embedded in it. as a result the plasticine reaches the floor at a horizontal distance of 0.25m away from the edge of the table.
1.whats the horizontal velocity of the plasticine given that the table surface is 0.6m high.?
2.whats the velocity of the pellet just before it hit the plasticine?
3.whats the velocity of the plasticine just before impact with the floor at the horizontal distance of 0.25m?
time to fall .6 meters:
time= sqrt(2h/g) where h=.6, g=9.8
horizonal velocity= distance/time=.25/timeabove
velocity before impact: (conservation of momentum)
vp*mp=(mp+50)*horizontalvelocityabove
solve for vp, mass pellet=.01kg mp
velocity of plasticine:
vertical velocity=g*timeinflight
velocity at impact= sqrt (verticalvelocity^2 + horizontalvelocityabove^2)
To determine the answers to the questions, we'll need to apply the principles of conservation of momentum and conservation of energy.
1. First, let's determine the horizontal velocity of the plasticine. Given that the pellet remains embedded in the plasticine, the total momentum before and after the collision remains the same.
The momentum of the pellet before the collision is calculated as the product of its mass (converted to kg) and its velocity, which we'll denote as v_p:
Momentum before = mass_p * v_p
= 0.01 kg * v_p
Since the pellet remains embedded in the plasticine, their combined mass after the collision is the sum of the pellet's mass and the plasticine's mass. We'll denote the combined mass as M:
M = mass_p + mass_plasticine
= 0.01 kg + 50 kg
To determine the velocity of the plasticine, we'll divide the momentum before the collision by the combined mass after the collision:
v_plasticine = Momentum before / M
= (0.01 kg * v_p) / (0.01 kg + 50 kg)
2. To find the velocity of the pellet just before it hit the plasticine, we need to consider conservation of energy. When the pellet is fired, it has both kinetic energy and potential energy due to its height above the ground. Assuming no energy losses due to air resistance, we can equate the initial potential energy to the final kinetic energy just before impact.
The initial potential energy of the pellet is given by mass_p * gravity * height, where gravity is approximately 9.8 m/s^2. Since the pellet is fired horizontally, it has no initial kinetic energy in the horizontal direction.
Just before impact, the pellet has kinetic energy due to its horizontal motion. We can calculate this using the kinetic energy formula: KE = 0.5 * mass_p * velocity_p^2, where velocity_p is the velocity just before impact.
Equating the initial potential energy to the final kinetic energy, we can solve for velocity_p:
mass_p * gravity * height = 0.5 * mass_p * velocity_p^2
Simplifying this equation, we find:
velocity_p = sqrt(2 * gravity * height)
3. To find the velocity of the plasticine just before impact with the floor at a horizontal distance of 0.25m, we can use the principle of conservation of energy again. Since no external horizontal forces act on the plasticine after it leaves the table, the sum of its initial potential energy and initial kinetic energy in the vertical direction equals its final kinetic energy just before impact.
The initial potential energy of the plasticine is given by mass_plasticine * gravity * height, and its initial velocity component in the vertical direction is 0. The final kinetic energy is given by 0.5 * mass_plasticine * velocity_plasticine^2, where velocity_plasticine is the velocity just before impact.
Equating the initial potential energy to the final kinetic energy, we have:
mass_plasticine * gravity * height = 0.5 * mass_plasticine * velocity_plasticine^2
To solve for velocity_plasticine, we rearrange the equation:
velocity_plasticine = sqrt(2 * gravity * height)
Remember to substitute the value of height as 0.6m into the equations for all three parts.