A 3kg mass moving initially to the right along the x axis with a speed of 8m/s makes a perfectly inelastic collision with a 5kg mass initially at rest at the origin.what fraction of the initial kinetic energy of the system is lost in the collision.what formula must i use.
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To determine the fraction of initial kinetic energy lost in the collision, you can use the conservation of momentum principle. This principle states that the total momentum before the collision is equal to the total momentum after the collision.
The formula for momentum is given by:
Momentum (p) = mass (m) × velocity (v)
Before the collision, the 3kg mass is moving with a velocity of 8m/s, and the 5kg mass is at rest (velocity = 0m/s). Therefore, the total momentum before the collision is:
Initial total momentum = (mass1 × velocity1) + (mass2 × velocity2)
= (3kg × 8m/s) + (5kg × 0m/s)
= 24kg·m/s
During a perfectly inelastic collision, the two masses stick together and move as a single entity after the collision. Let's call their final velocity as 'vf'. The total momentum after the collision is:
Final total momentum = (mass1 + mass2) × vf
Since the two masses are sticking together, their combined mass after the collision is 3kg + 5kg = 8kg. Therefore,
Final total momentum = 8kg × vf
According to the conservation of momentum principle, the initial total momentum equals the final total momentum, so we have:
Initial total momentum = Final total momentum
24kg·m/s = 8kg × vf
To find the velocity (vf) after the collision, we can rearrange the equation as follows:
vf = 24kg·m/s ÷ 8kg
vf = 3m/s
Now, we can calculate the kinetic energy before and after the collision to determine the fraction of lost energy.
The formula for kinetic energy is:
Kinetic energy (KE) = (1/2) × mass × velocity^2
Before the collision, the initial kinetic energy of the system is given by:
Initial KE = (1/2) × mass1 × velocity1^2 + (1/2) × mass2 × velocity2^2
= (1/2) × 3kg × (8m/s)^2 + (1/2) × 5kg × (0m/s)^2
= (1/2) × 3kg × 64m^2/s^2 + 0
= 96J
After the collision, the final kinetic energy of the system is given by:
Final KE = (1/2) × (mass1 + mass2) × vf^2
= (1/2) × 8kg × (3m/s)^2
= (1/2) × 8kg × 9m^2/s^2
= 36J
The fraction of energy lost in the collision is calculated by dividing the difference between initial and final kinetic energy by the initial kinetic energy:
Fraction of energy lost = (Initial KE - Final KE) / Initial KE
= (96J - 36J) / 96J
= 60J / 96J
= 5/8
Therefore, the fraction of initial kinetic energy lost in the collision is 5/8 or approximately 0.625.