1. A 4.0 N force acts for 3 seconds on an object. The force suddenly increases to 15 N and acts for one more second. What impulse was imparted by these forces to the object?
2. A railroad freight car, mass 15,000 kg, is allowed to coast along a level track at a speed of 2 m/s. It collides and couples with a 50,000 kg second car, initially at rest and with brakes released. What is the speed of the two cars after coupling?
3. Lonnie pictches a baseball of mass .2 kg. The ball arrives at home plate with a speed of 40 m/s and is batted straight back to Lonnie with a return speed of 60 m/s. If the bat is in contact with the ball for .050 s, what is the impulse experienced by the ball?
4. Alex throws a .15 kg rubber ball down onto a steel plate. The ball's speed just before the impact 6.5 m/s, and just after is 3.5 m/s. What is the change in the magnitude of the balls momentum??
ANY HELP WILL BE APPRECIATED.Thanks!
1. Add the two impulses.
2. Apply the law of conservation of total momentum
3. The impulse equals the momentum change. Changing the direction of motion changes the sign
4. Subtract the final momentum from the initial momentum. Make sure you get the sign right on the final momentum
I will be happy to critique your work.
1. i got 27
2. i got .46
3.still confused
4. "
1. Correct, but you should include the units, Newton-seconds or kg m/s
2. Correct, but you should include the units of m/s
could you expand on 3 and 4 please?
3. The momentum change is .2(40+60) = 20 kg m/s. That equals the impulse. You do not need to know the contact time to get the impulse.
4. Do it the same way as 3
1. Well, it seems like this object is in for a ride! First, a 4 N force is applied for 3 seconds, then suddenly BAM, it increases to 15 N for one more second. Talk about a rollercoaster of forces! To find the impulse, we can use the equation: impulse = force × time. So, for the first force: impulse = 4 N × 3 s = 12 Ns. And for the second force: impulse = 15 N × 1 s = 15 Ns. Therefore, the total impulse imparted by these forces is 12 Ns + 15 Ns = 27 Ns. Hang on tight, object!
2. Imagine two railroad cars getting cozy and coupling up! Let's see what happens. The first car has a mass of 15,000 kg and a speed of 2 m/s. The second car is a bit heavier, weighing in at 50,000 kg, and it starts at rest. After they couple, we need to find their final speed. Now, this may sound strange, but momentum is conserved in this situation. So we can say the initial momentum of the first car is equal to the final momentum of the two cars together. The initial momentum is mass × velocity, so it's (15,000 kg × 2 m/s). The final momentum is (15,000 kg + 50,000 kg) × the final speed. Now let's solve for the final speed. (15,000 kg × 2 m/s) = (65,000 kg × final speed). Dividing both sides by 65,000 kg, we get the final speed = (15,000 kg × 2 m/s) ÷ 65,000 kg. After some calculations, the final speed of the two cars after coupling is about 0.4615 m/s. They're not going too fast, but hey, at least they found each other!
3. Ah, the pitcher's dilemma. Lonnie throws a baseball weighing 0.2 kg at 40 m/s, and then it's batted straight back to him at 60 m/s. We want to find the impulse experienced by the ball. Impulse is the change in momentum, which is mass × change in velocity. The initial momentum is (0.2 kg × 40 m/s), and the final momentum is (0.2 kg × -60 m/s). Why negative? Well, the ball is going in the opposite direction after being batted. Now, let's find the impulse by subtracting the initial momentum from the final momentum: Impulse = (0.2 kg × -60 m/s) - (0.2 kg × 40 m/s). After doing the math, the impulse experienced by the ball is -16 kg·m/s. Looks like Lonnie and the ball shared some negative vibes!
4. Alex decides to give a rubber ball a taste of gravity by throwing it down onto a steel plate. The ball's speed just before the impact is 6.5 m/s, and right after the impact, it slows down to 3.5 m/s. We want to find the change in the magnitude of the ball's momentum. Momentum is equal to mass × velocity, and we want the change in momentum, so we need to calculate the difference between the initial and final momenta. The initial momentum is (0.15 kg × 6.5 m/s), and the final momentum is (0.15 kg × 3.5 m/s). To find the change in momentum, we subtract the initial momentum from the final momentum: Change in momentum = (0.15 kg × 3.5 m/s) - (0.15 kg × 6.5 m/s). After the calculation, the change in the magnitude of the ball's momentum is about -0.45 kg·m/s. Well, that's one way to leave an impact!
1. To find the impulse imparted by the forces on the object, we need to calculate the change in momentum of the object.
Momentum is defined as the product of an object's mass and its velocity. The formula for momentum is:
Momentum = mass × velocity
In the first phase, where a 4.0 N force acts for 3 seconds, we need to calculate the momentum:
Momentum1 = force1 × time1
Given that force1 = 4.0 N and time1 = 3 s, we can calculate momentum1.
In the second phase, where a 15 N force acts for 1 second, we also need to calculate the momentum:
Momentum2 = force2 × time2
Given force2 = 15 N and time2 = 1 s, we can calculate momentum2.
The total impulse imparted to the object is the change in momentum, which can be found by subtracting the initial momentum from the final momentum:
Impulse = momentum2 - momentum1
2. To find the speed of the two cars after coupling, we can use the principle of conservation of momentum. According to this principle, the total momentum before the collision should be equal to the total momentum after the collision.
The momentum of an object is given by the product of its mass and velocity:
Momentum = mass × velocity
Considering the two cars, the total momentum before collision is:
Total momentum before collision = momentum car 1 + momentum car 2
Here, car 1 has a mass of 15,000 kg and is moving at a speed of 2 m/s. Car 2 has a mass of 50,000 kg and is initially at rest. Therefore, the momentum of car 2 is zero.
Total momentum before collision = momentum car 1 + momentum car 2 = (mass car 1 × velocity car 1) + (mass car 2 × velocity car 2)
= (15,000 kg × 2 m/s) + (50,000 kg × 0 m/s)
After the collision, the two cars couple and move together. Let the common final velocity of the coupled cars be v. Therefore, the total momentum after collision is:
Total momentum after collision = (mass car 1 + mass car 2) × velocity after collision
Substituting the mass and velocity values, we can calculate the final velocity of the coupled cars.
3. To find the impulse experienced by the ball, we can use the formula:
Impulse = change in momentum
We know the initial momentum of the ball when it is pitched is equal to the mass of the ball multiplied by its initial velocity. The final momentum of the ball when it is batted back is equal to the mass of the ball multiplied by its return velocity. The change in momentum is the difference between the final and initial momentum:
Impulse = (mass × return velocity) - (mass × initial velocity)
Given the mass of the ball, initial velocity, and return velocity, we can calculate the impulse experienced by the ball.
4. The change in the magnitude of the ball's momentum can be found using the equation:
Change in momentum = final momentum - initial momentum
Momentum is calculated as the product of an object's mass and velocity. The final momentum is the product of the mass of the ball and its final velocity, while the initial momentum is the product of the mass and initial velocity.
Therefore, the equation becomes:
Change in momentum = (mass × final velocity) - (mass × initial velocity)
Given the mass of the ball, initial velocity, and final velocity, we can calculate the change in the magnitude of the ball's momentum.