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!
duplicate post. Same answer
1. To calculate the impulse imparted by a force on an object, we can use the equation:
Impulse = Force × Time
In this case, we have two forces acting on the object for different durations. So, we need to calculate the impulse for each force separately and then add them together to get the total impulse.
First, let's calculate the impulse for the initial force of 4.0 N acting for 3 seconds:
Impulse1 = Force1 × Time1
= 4.0 N × 3 s
= 12 N·s
Next, let's calculate the impulse for the second force of 15 N acting for 1 second:
Impulse2 = Force2 × Time2
= 15 N × 1 s
= 15 N·s
Finally, we can find the total impulse by adding the individual impulses together:
Total Impulse = Impulse1 + Impulse2
= 12 N·s + 15 N·s
= 27 N·s
Therefore, the total impulse imparted by these forces to the object is 27 N·s.
2. To solve this problem, we can apply the principle of conservation of momentum, which states that the total momentum before a collision is equal to the total momentum after the collision.
Before the collision, the first car has a mass of 15,000 kg and a speed of 2 m/s. The second car has a mass of 50,000 kg and is initially at rest. Let's denote the final speed of both cars after coupling as v.
Using the conservation of momentum equation:
Total momentum before collision = Total momentum after collision
(mass of first car × initial velocity of first car) + (mass of second car × initial velocity of second car)
= (mass of first car + mass of second car) × final velocity
(15,000 kg × 2 m/s) + (50,000 kg × 0 m/s) = (15,000 kg + 50,000 kg) × v
30,000 kg·m/s = 65,000 kg × v
Now, we can solve for v:
v = (30,000 kg·m/s) / (65,000 kg)
≈ 0.462 m/s
Therefore, the speed of the two cars after coupling is approximately 0.462 m/s.
3. To find the impulse experienced by the ball, we can use the equation:
Impulse = Change in momentum
The momentum of an object is given by the equation:
Momentum = Mass × Velocity
Given that the mass of the baseball is 0.2 kg and it goes from a speed of 40 m/s to 60 m/s during contact with the bat, we can calculate the change in momentum.
Initial momentum of the ball = Mass × Initial velocity
= 0.2 kg × 40 m/s
= 8 kg·m/s
Final momentum of the ball = Mass × Final velocity
= 0.2 kg × 60 m/s
= 12 kg·m/s
Change in momentum = Final momentum - Initial momentum
= 12 kg·m/s - 8 kg·m/s
= 4 kg·m/s
Therefore, the impulse experienced by the ball is 4 kg·m/s.
4. The change in the magnitude of an object's momentum can be calculated using the equation:
Change in momentum = Final momentum - Initial momentum
Given that the mass of the rubber ball is 0.15 kg and its speed changes from 6.5 m/s to 3.5 m/s, we can calculate the change in momentum.
Initial momentum of the ball = Mass × Initial velocity
= 0.15 kg × 6.5 m/s
= 0.975 kg·m/s
Final momentum of the ball = Mass × Final velocity
= 0.15 kg × 3.5 m/s
= 0.525 kg·m/s
Change in momentum = Final momentum - Initial momentum
= 0.525 kg·m/s - 0.975 kg·m/s
= -0.45 kg·m/s
The negative sign indicates that the direction of the momentum has changed.
Therefore, the change in the magnitude of the ball's momentum is 0.45 kg·m/s.