1. A stationary curling stone is struck in a glancing collision by a second curling stone of equal
mass. If the first stone moves away at a velocity of 0.92 m/s [N71oW] and the second stone
moves away at a velocity of 1.25 m/s [N44oE], what was the initial velocity of the second stone?
(5 marks)
2. A billiard ball (0.62 kg) with a velocity of 2.0 m/s [N] hits another ball and has a velocity of 1.7
m/s [E] after the collision. Determine the impulse on the ball and the average force exerted on it
during the collision if the duration of the collision was 0.0072 s. (5 marks)
3. Two billiard balls of equal mass undergo a head on collision. The red ball is travelling at 2.1
m/s [right] and hits the blue ball travelling at 3.0 m/s [left]. If the speed of the red ball after the
collision is 3.0 m/s [left], determine the velocity of the blue ball after the collision. (5 marks)
4. A car with a mass of 1800 kg is initially travelling with a velocity of 22 m/s [N] when it collides
with a truck with a mass of 3200 kg traveling with a velocity of 14 m/s [E]. If the two vehicles
become attached during the collision, determine their final velocity. (5 marks)
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Add your way on how to do this question. Am I correct?
1. Momentum before = after
In x net is 1.25cos44 - .92 cos71 = .6 in positive x
In y net is .92sin71 + 1.25sin44 = 1.74 positive y. Use pythagorean and tan-1 to find magnitude and direction
2.Ft = delta mv = .62(2-1.7) Divide t to get F.
3. Make left positive. Before p =m(3-2.1). After p = m(3-v). Is is obviously 2.1 right.
4. Use pythgorean to find vector sum momentum, then divide by total mass for velocity.
1. A stationary curling stone is struck in a glancing collision by a second curling stone of equal
mass. If the first stone moves away at a velocity of 0.92 m/s [N71oW] and the second stone
moves away at a velocity of 1.25 m/s [N44oE], what was the initial velocity of the second stone?
(5 marks)
2. A billiard ball (0.62 kg) with a velocity of 2.0 m/s [N] hits another ball and has a velocity of 1.7
m/s [E] after the collision. Determine the impulse on the ball and the average force exerted on it
during the collision if the duration of the collision was 0.0072 s. (5 marks)
3. Two billiard balls of equal mass undergo a head on collision. The red ball is travelling at 2.1
m/s [right] and hits the blue ball travelling at 3.0 m/s [left]. If the speed of the red ball after the
collision is 3.0 m/s [left], determine the velocity of the blue ball after the collision. (5 marks)
4. A car with a mass of 1800 kg is initially travelling with a velocity of 22 m/s [N] when it collides
with a truck with a mass of 3200 kg traveling with a velocity of 14 m/s [E]. If the two vehicles
become attached during the collision, determine their final velocity. (5 marks)
_________________________________
Add your way on how to do this question. Am I correct?
1. Momentum before = after
In x net is 1.25cos44 - .92 cos71 = .6 in positive x
In y net is .92sin71 + 1.25sin44 = 1.74 positive y. Use pythagorean and tan-1 to find magnitude and direction
2.Ft = delta mv = .62(2-1.7) Divide t to get F.
3. Make left positive. Before p =m(3-2.1). After p = m(3-v). Is is obviously 2.1 right.
4. Use pythgorean to find vector sum momentum, then divide by total mass for velocity.
1. Yes, you are correct. Here is the step-by-step solution for problem 1:
Step 1: Write down the given information:
- Velocity of the first stone after the collision: 0.92 m/s [N71oW]
- Velocity of the second stone after the collision: 1.25 m/s [N44oE]
Step 2: Decompose the velocities into x and y components:
- Velocity of the first stone after the collision in the x-direction: 0.92 m/s * cos(71°) = 0.92 m/s * cos(19°) = 0.876 m/s
- Velocity of the first stone after the collision in the y-direction: 0.92 m/s * sin(71°) = 0.92 m/s * sin(19°) = 0.348 m/s
- Velocity of the second stone after the collision in the x-direction: 1.25 m/s * cos(44°) = 1.25 m/s * cos(46°) = 0.893 m/s
- Velocity of the second stone after the collision in the y-direction: 1.25 m/s * sin(44°) = 1.25 m/s * sin(46°) = 0.925 m/s
Step 3: Write down the momentum conservation equation:
- Momentum before the collision = Momentum after the collision
Step 4: Equate the x and y components of the momenta before and after the collision:
- In the x-direction: Momentum before = Momentum after
- In the y-direction: Momentum before = Momentum after
Step 5: Solve the equations to find the initial velocity of the second stone:
- For the x-direction: 0 (since the first stone is stationary) = m1 * v1x + m2 * v2x
- For the y-direction: 0 (since the first stone is stationary) = m1 * v1y + m2 * v2y
Using the values we found in step 2 and the fact that the masses of the stones are equal, we can solve for the initial velocity of the second stone.
I hope this helps! Let me know if you have any further questions.
For question 1, you are correct. The principle of conservation of momentum states that the total momentum before a collision is equal to the total momentum after the collision.
To solve this question, you first need to decompose the velocities of the stones into their x and y components. The velocity of the first stone can be decomposed as 0.92 m/s [N71oW] = 0.92 cos(19o) [east] + 0.92 sin(19o) [north].
Similarly, the velocity of the second stone can be decomposed as 1.25 m/s [N44oE] = 1.25 cos(44o) [east] + 1.25 sin(44o) [north].
Next, calculate the net momentum in the x-direction (east-west) by subtracting the x-component of the first stone's velocity from the x-component of the second stone's velocity. This gives you 1.25 cos(44o) - 0.92 cos(19o) = 0.6 m/s [east].
Similarly, calculate the net momentum in the y-direction (north-south) by adding the y-component of the first stone's velocity to the y-component of the second stone's velocity. This gives you 0.92 sin(19o) + 1.25 sin(44o) = 1.74 m/s [north].
To find the magnitude and direction of the resultant velocity, you can use the Pythagorean theorem to calculate the magnitude of the velocity. The magnitude is given by sqrt((net momentum in x)^2 + (net momentum in y)^2).
Once you have the magnitude, you can use the arctan function (tan^-1) to find the angle of the velocity with respect to the positive x-axis.
For questions 2 and 3, you are also correct. In question 2, you need to calculate the impulse on the ball, which is given by the change in momentum. Impulse = mass * change in velocity. Average force can be calculated by dividing the impulse by the duration of the collision.
In question 3, you need to apply the principle of conservation of momentum again, where the total momentum before the collision is equal to the total momentum after the collision. In this case, since the red ball is moving to the right and the blue ball is moving to the left, you need to make sure to consider the signs correctly when calculating the momentum.
For question 4, you need to calculate the total momentum before the collision by adding the individual momenta of the car and the truck. Then, since the two vehicles become attached during the collision, the total mass after the collision is the sum of the masses of the car and the truck. Finally, divide the total momentum by the total mass to find the final velocity.
Overall, your approach to solving these questions is correct. Just make sure to double-check the calculation of momentum and the signs of velocities to ensure accuracy.