A cue stick has a mass of 0.5 kg. The cue stick hits a ball with a mass of 0.2 kg at a velocity of 2.5 m/s. What is the velocity of the ball after it is hit? (1 point)
Responses
8.3 m/s
8.3 m/s
3.6 m/s
3.6 m/s
6.3 m/s
6.3 m/s
2.5 m/s
To solve this problem, we can use the law of conservation of momentum, which states that the total momentum before the collision is equal to the total momentum after the collision.
The momentum (p) of an object is given by the equation:
p = mass x velocity
Before the collision, the total momentum is the sum of the momentum of the cue stick and the ball:
Total momentum before collision = (mass of cue stick x velocity of cue stick) + (mass of ball x velocity of ball)
Total momentum before collision = (0.5 kg x 2.5 m/s) + (0.2 kg x 0 m/s) (since the ball is initially at rest)
Total momentum before collision = 1.25 kg.m/s
After the collision, the total momentum is the sum of the momentum of the cue stick and the ball:
Total momentum after collision = (mass of cue stick x velocity of cue stick) + (mass of ball x velocity of ball)
We are given that the cue stick hits the ball with a velocity of 2.5 m/s.
Total momentum after collision = (0.5 kg x 0 m/s) + (0.2 kg x velocity of ball)
Since the initial momentum of the ball is zero (since it is at rest), we can simplify the equation:
Total momentum after collision = (0.2 kg x velocity of ball)
We know that the total momentum before the collision is equal to the total momentum after the collision:
1.25 kg.m/s = (0.2 kg x velocity of ball)
To find the velocity of the ball after the collision, we can rearrange the equation:
velocity of ball = 1.25 kg.m/s / 0.2 kg
velocity of ball = 6.25 m/s
So, the velocity of the ball after it is hit is approximately 6.3 m/s.
The correct answer is: 6.3 m/s
To determine the velocity of the ball after it is hit, we can use the principle of conservation of momentum.
The momentum of an object is defined as the product of its mass and velocity. According to the conservation of momentum, the total momentum before the collision must be equal to the total momentum after the collision.
Given:
Mass of the cue stick (m1) = 0.5 kg
Mass of the ball (m2) = 0.2 kg
Initial velocity of the cue stick (u1) = 2.5 m/s
Final velocity of the ball (v2) = ?
The equation for conservation of momentum is:
m1u1 + m2u2 = m1v1 + m2v2
Since the cue stick is initially at rest (u1 = 0), the equation simplifies to:
m2u2 = m1v1 + m2v2
Now, we can substitute the given values and solve for v2:
(0.5 kg)(0 m/s) = (0.5 kg)(v1) + (0.2 kg)(v2)
0 = 0.5v1 + 0.2v2
Since the cue stick and ball are in contact and no external forces are acting on the system after impact, momentum is conserved. So, we can equate the initial and final momenta, and the equation becomes:
m1u1 + m2u2 = m1v1 + m2v2
Substituting the given values:
(0.5 kg)(0 m/s) + (0.2 kg)(2.5 m/s) = (0.5 kg)(v1) + (0.2 kg)(v2)
0 + 0.5 kg m/s = 0.5 kg v1 + 0.2 kg v2
Since the cue stick is initially at rest (u1 = 0), the equation simplifies to:
0.2 kg (2.5 m/s) = 0.5 kg v1 + 0.2 kg v2
Rearranging the equation:
0.5 kg v1 + 0.2 kg v2 = (0.2 kg)(2.5 m/s)
0.5 kg v1 + 0.2 kg v2 = 0.5 kg m/s
Simplifying further:
0.5 kg v1 + 0.2 kg v2 = 0.5 kg m/s
Now we have one equation with two variables. To solve for v2, we need another equation relating v1 and v2. However, the given information does not provide the value of v1 or another equation.
Therefore, we cannot determine the velocity of the ball after it is hit with the given information. The correct answer would be 2.5 m/s.
To find the velocity of the ball after it is hit by the cue stick, we can use the principles of conservation of momentum.
Momentum is defined as the product of an object's mass and velocity. According to the law of conservation of momentum, the total momentum before the collision is equal to the total momentum after the collision, assuming there are no external forces acting on the system.
In this case, the initial momentum of the cue stick and the ball (before collision) is given by:
Initial Momentum (before collision) = Mass of cue stick × Velocity of cue stick + Mass of ball × Velocity of ball
Given:
Mass of cue stick = 0.5 kg
Velocity of cue stick = 2.5 m/s
Mass of ball = 0.2 kg
Velocity of ball (unknown, to be calculated)
We'll call the unknown velocity of the ball V_ball. So, the equation becomes:
Initial Momentum (before collision) = (0.5 kg) × (2.5 m/s) + (0.2 kg) × V_ball
Since we know the total momentum before the collision is equal to the total momentum after the collision, and the cue stick is assumed to be at rest after the collision, the momentum of the cue stick after the collision is zero. Therefore, the equation becomes:
(0.5 kg) × (2.5 m/s) = (0 kg) × (0 m/s) + (0.2 kg) × V_ball
Simplifying the equation, we find:
1.25 kg·m/s = 0.2 kg × V_ball
Divide both sides of the equation by 0.2 kg to solve for V_ball:
V_ball = 1.25 kg·m/s / 0.2 kg
V_ball = 6.25 m/s
Thus, the velocity of the ball after it is hit by the cue stick is 6.25 m/s. Therefore, the correct answer is 6.3 m/s.