250 g ball of putty moving horizontally at 9 m/s collides with and sticks to a block lying on a frictionless horizontal surface. If 20%of the kinetic energy is lost, what is the mass of the block?
What i did
Mass1 = 0.25 kg
Mass 2 =?
Kinetic initial = 1/2(0.25)(9)^2 = 10.125 J
Kinetic final = 10.125-20% = 8.1 J
But now i don't know how to find the mass of object 2
Two eq, two unknown:
.25(9) = (.25+m2)vf
1/2(.25 + m2)vf^2 = 8.1
pp
Is there anything else I can assist you with?
Well, it seems like you've got yourself in a bit of a sticky situation there. But don't worry, I'm here to help you out!
Since the ball sticks to the block after the collision, we can use the principle of conservation of momentum to solve this problem. This principle states that the total momentum before the collision is equal to the total momentum after the collision.
So let's start by calculating the initial momentum of the ball:
Momentum initial = Mass of the ball * Velocity of the ball
= 0.25 kg * 9 m/s
= 2.25 kg*m/s
Since the block is initially at rest, its initial momentum is zero.
After the collision, the ball and the block stick together, so their final velocity will be the same. Let's call this common velocity "vf". The total mass after the collision will be the sum of the mass of the ball and the mass of the block.
So, the final momentum after the collision will be:
Momentum final = (Mass of the ball + Mass of the block) * vf
Since momentum is conserved, we can equate the initial momentum to the final momentum:
Momentum initial = Momentum final
2.25 kg*m/s = (0.25 kg + Mass of the block) * vf
Now, we know that the initial kinetic energy is 10.125 J and the final kinetic energy is 8.1 J. We can use the relationship between kinetic energy and momentum to find vf.
Kinetic energy = (1/2) * Mass * vf^2
Plugging in the numbers:
8.1 J = (1/2) * (0.25 kg + Mass of the block) * vf^2
Now you can solve this equation to find the value of vf. Once you have vf, you can back-calculate the mass of the block by using the equation Momentum final = (Mass of the ball + Mass of the block) * vf.
Hope this helps you bounce back from your confusion!
To find the mass of object 2 (the block), we can use the conservation of momentum principle. According to this principle, the total momentum before the collision is equal to the total momentum after the collision.
The momentum of an object is given by the product of its mass and velocity.
Let's assume the initial velocity of the block is zero since it's lying on the surface and not moving initially.
The initial momentum before the collision is therefore the momentum of the ball of putty, which is given by:
Momentum initial = Mass 1 * Velocity 1
= 0.25 kg * 9 m/s
Now, since the ball of putty collides and sticks to the block, they move together after the collision. This means their final velocity is the same. Let's denote this final velocity as v_f.
The momentum after the collision is then given by:
Momentum final = (Mass 1 + Mass 2) * Velocity final
= (0.25 kg + Mass 2) * v_f
Since the total momentum before and after the collision is the same, we can equate the two expressions:
Mass 1 * Velocity 1 = (Mass 1 + Mass 2) * v_f
0.25 kg * 9 m/s = (0.25 kg + Mass 2) * v_f
Now, we also know that kinetic energy is lost during the collision. The kinetic energy before the collision is given by:
Kinetic initial = 1/2 * Mass 1 * (Velocity 1)^2
= 1/2 * 0.25 kg * (9 m/s)^2
And the kinetic energy after the collision is given by:
Kinetic final = 1/2 * (Mass 1 + Mass 2) * (v_f)^2
We are told that 20% of the kinetic energy is lost. This means the kinetic final energy is 80% of the initial energy:
Kinetic final = 0.8 * Kinetic initial
1/2 * (Mass 1 + Mass 2) * (v_f)^2 = 0.8 * 1/2 * Mass 1 * (Velocity 1)^2
Now, we have two equations:
0.25 kg * 9 m/s = (0.25 kg + Mass 2) * v_f
1/2 * (Mass 1 + Mass 2) * (v_f)^2 = 0.8 * 1/2 * Mass 1 * (Velocity 1)^2
We can solve these equations simultaneously to find the mass of the block (Mass 2). By substituting the values for Mass 1, Velocity 1, and solving the equations, we can find the mass of the block.