A 0.25-kg punk, Initially at rest on a frictionless horizontal surface, is struck by a 0.20kg punk that is initially moving along the x-axis with a velocity of 2.20 m/sec. After the collision, the 0.20 kg punk has a speed of 1.5 m/s at an angle of 37 to the positive x-axis. Calculate:
A.The velocity of the .25 kg punk after collision
B.The angle of the second punk
C.The total energy before and after collision.
D.What is the percentage of energy lost in this collision?
A. M1*V1 + M2*V2 = M1*V3 + M2*V4
0.25*0+0.20*2.20=0.25*V3 + 0.20*1.5[37]
0.44 = 0.25V3 + 0.3[37o]
0.44 = 0.25V3 + 0.3*Cos37 + i0.3*sin37
0.44 = 0.25V3 + 0.240 + 0.181i
-0.25V3 = 0.240 - 0.44 + 0.181i
= -0.25V3 = -0.20 + 0.181i
V3 = 0.8 - 0.734i
V3 = sqrt(0.8^2+0.734^2) = 1.18 m/s. =
Velocity of 0.25 kg puck.
B. Tan A = Y/X = -0.734/0.8 = -0.9175
A = -42.5o, CW = 317o, CCW. = Direction
of the 0.25 kg puck.
C. KE1 = 0.5M2*V2^2 = 0.5*0.2*2.2^2 = 0.484 J.
KE2 = 0.5M1*V3^2 + 0.5M2*V4^2
KE2 = 0.5*0.25*1.18^2 + 0.5*0.2*1.5^2 =
0.202 J.
D. ((KE1-KE2)/KE1)* 100%
To solve this problem, we will use the principles of conservation of momentum and conservation of kinetic energy.
A. To calculate the velocity of the 0.25 kg punk after the collision, we need to use the conservation of momentum. The initial momentum before the collision is equal to the final momentum after the collision.
Step 1: Calculate the initial momentum of 0.20 kg punk.
Initial momentum = mass x velocity = 0.20 kg x 2.20 m/s = 0.44 kg⋅m/s
Step 2: Calculate the final momentum of the two punks.
Final momentum = mass x velocity = (0.20 kg x 1.5 m/s) + (0.25 kg x v)
Since we're assuming momentum is conserved, we can write the equation as:
0.44 kg⋅m/s = (0.20 kg x 1.5 m/s) + (0.25 kg x v)
Solving for v, the velocity of the 0.25 kg punk after the collision:
v = (0.44 kg⋅m/s - 0.30 kg⋅m/s) / 0.25 kg
v = 0.14 kg⋅m/s / 0.25 kg
v = 0.56 m/s
Therefore, the velocity of the 0.25 kg punk after the collision is 0.56 m/s.
B. To calculate the angle of the second punk after the collision, we can use trigonometry. The angle can be determined using the components of the velocity provided.
tan(θ) = v_y / v_x
Given:
v = 1.5 m/s
θ = 37 degrees
Step 1: Calculate the vertical component of the velocity (v_y).
v_y = v * sin(θ)
v_y = 1.5 m/s * sin(37 degrees)
Step 2: Calculate the horizontal component of the velocity (v_x).
v_x = v * cos(θ)
v_x = 1.5 m/s * cos(37 degrees)
So, the velocity of the second punk can be represented as:
v = v_x i + v_y j
Therefore, the angle of the second punk after the collision is given by:
tan(θ) = v_y / v_x
θ = arctan(v_y / v_x)
θ = arctan(v_y / v_x)
θ = arctan(sin(37 degrees) / cos(37 degrees))
Solve the above equation to find the angle.
C. To calculate the total energy before and after the collision, we'll use the principle of conservation of energy. The total energy before the collision is equal to the total energy after the collision.
Step 1: Calculate the initial kinetic energy of the system.
Initial kinetic energy = 1/2 * m1 * v1^2 + 1/2 * m2 * v2^2
m1 = 0.20 kg
v1 = 2.20 m/s
m2 = 0.25 kg
v2 = 0 m/s (since the 0.25 kg punk is initially at rest)
Step 2: Calculate the final kinetic energy of the system.
Final kinetic energy = 1/2 * m1 * v3^2 + 1/2 * m2 * v^2
v3 = 1.5 m/s (velocity of the second punk after collision)
v = 0.56 m/s (velocity of the 0.25 kg punk after collision)
D. To calculate the percentage of energy lost in this collision:
Percentage of energy lost = (Initial energy - Final energy) / Initial energy * 100%
Plug in the values and calculate the percentage.
To solve this problem, we can use the concepts of conservation of momentum and conservation of kinetic energy.
A. The velocity of the 0.25 kg punk after the collision:
We can start by calculating the momentum of each punk before and after the collision.
The initial momentum of the 0.25 kg punk (p1) is zero since it is initially at rest.
The initial momentum of the 0.20 kg punk (p2) can be calculated using the equation:
p = m * v
where p is momentum, m is mass, and v is velocity.
So, p2 = 0.20 kg * 2.20 m/s = 0.44 kg·m/s.
Now, let's analyze the momentum after the collision.
The final momentum of the 0.25 kg punk (p1') can be calculated using the equation:
p1' = m1' * v1'
where m1' is the mass of the 0.25 kg punk after the collision and v1' is its velocity.
Let's assume the velocity of the 0.25 kg punk after the collision is v1'.
Similarly, the final momentum of the 0.20 kg punk (p2') can be calculated using the equation:
p2' = m2' * v2'
where m2' is the mass of the 0.20 kg punk after the collision and v2' is its velocity.
The velocity of the 0.20 kg punk after the collision is given as 1.5 m/s, but we need to find its x-component and y-component velocities.
Since we know the speed (1.5 m/s) and the angle (37°), we can use trigonometry to find the x-component and y-component velocities. Let's call the x-component velocity of the 0.20 kg punk after the collision as vx' and the y-component velocity as vy'.
vx' = v2' * cos(angle) = 1.5 m/s * cos(37°)
vy' = v2' * sin(angle) = 1.5 m/s * sin(37°)
Now, let's analyze the conservation of momentum:
Before the collision: p1 + p2 = 0
After the collision: p1' + p2' = 0
Since the surface is frictionless, we can ignore the horizontal component of momentum. Thus, we only need to consider the x-component of momentum during calculations.
p1' + p2' = (m1' * v1') + (m2' * vx')
Since p1' is unknown, let's denote it as p1' = m1' * v1'
The equation can be written as:
p1' + p2' = p1' + (m2' * vx')
From conservation of momentum:
0.44 kg·m/s = m1' * v1' + (0.20 kg * vx')
We also know that the masses of both punks remain constant during the collision, so m1' = 0.25 kg and m2' = 0.20 kg.
So, the equation becomes:
0.44 kg·m/s = 0.25 kg * v1' + (0.20 kg * vx')
Now, we need to solve for v1'.
B. The angle of the second punk (v2'):
We already calculated the x-component (vx') and y-component (vy') velocities of the 0.20 kg punk after the collision using trigonometry:
vx' = v2' * cos(angle) = 1.5 m/s * cos(37°)
vy' = v2' * sin(angle) = 1.5 m/s * sin(37°)
Since we know the x-component (vx') and y-component (vy') velocities, we can use trigonometry to find the angle.
Using the equation:
angle = arctan(vy'/vx')
C. The total energy before and after the collision:
The total energy before and after the collision can be calculated using the equations:
Total energy before collision = 1/2 * m1 * v1^2 + 1/2 * m2 * v2^2
Total energy after collision = 1/2 * m1' * v1'^2 + 1/2 * m2' * v2'^2
D. The percentage of energy lost in this collision:
The percentage of energy lost in this collision can be calculated using the equation:
Percentage of energy lost = ((Total energy before collision - Total energy after collision) / Total energy before collision) * 100