A 6 kg bowling ball rolling at 5 m/s strikes a stationary 4 kg bowling ball. If ball #1 is moving forward at 2 m/s after the collision, what is the speed and direction of ball #2? What is the impulse of the system? If the collision last for .5 seconds, how much force is exerted?
Initial momentum = 6*5 = 30 kg m/s
Final momentum is therefore 30
30 = 6*2 + 4*v
4 v = 18
v = 4.5 m/s forward
There is no change of momentum of the system so no impulse for the system.
However there is a change of momentum or impulse for Ball 2 of 18 kg m/s
Force = change of momentum or impulse / time
=18/.5 = 36 Newtons
A cannon that is 10m long is designed to launch a 10kg ball over a castle wall.
In order to do this the ball must have a speed of at least 50m/s as it exits the
cannon. For every 10kg of explosives used, the force on the ball in the cannon
increases by 1000N. How many kg of explosives should they use?
2 Gravitation(100pts.)
Oh, bowling balls colliding! That's going to be a strikingly funny situation! Let's solve it with a touch of humor, shall we?
To find the speed and direction of ball #2, we need to use the principle of conservation of momentum. Since ball #1 is moving forward with a velocity of 2 m/s after the collision, we can assume that ball #2 moves backward, because they like to do the opposite of what their counterparts do.
Using the equation m1v1 + m2v2 = m1v1' + m2v2', we can plug in the given values: 6 kg * 5 m/s + 4 kg * 0 m/s = 6 kg * 2 m/s + 4 kg * v2'. We just need to solve for v2' now.
Let me grab my joke book for a moment... Ah, here it is: Why don't bowling balls join stand-up comedy? Because they always end up in a split!
Solving the equation, we find v2' = (6 kg * 5 m/s + 4 kg * 0 m/s - 6 kg * 2 m/s) / 4 kg. Simplifying that, we get v2' = -3.5 m/s. So, ball #2 is moving backward with a speed of 3.5 m/s.
Now, let's move on to the impulse of the system. Impulse is the change in momentum, which is given by the equation J = m1v1' - m1v1. Substituting the values we know, we get J = 6 kg * 2 m/s - 6 kg * 5 m/s. Let's crunch some numbers here... J = -18 kg·m/s. Negative impulse? That collision came as a total surprise!
Lastly, let's calculate the force exerted during the collision using the equation F = J / t, where t represents the time duration of the collision. Plugging in the numbers: F = -18 kg·m/s / 0.5 s. This gives us F = -36 N. Negative force? Woah, those bowling balls really went rogue!
So, there you have it! Ball #2 is moving backward at 3.5 m/s, the impulse is -18 kg·m/s, and the force exerted during the collision is -36 N. Better keep an eye out for those wild bowling balls next time!
To solve this problem, we can use the principles of conservation of momentum and impulse.
1. Let's start by calculating the initial momentum of ball #1 before the collision and the total initial momentum of the system:
Momentum (p) = mass (m) × velocity (v)
Initial momentum of ball #1 = 6 kg × 5 m/s = 30 kg·m/s
Initial momentum of the system = initial momentum of ball #1 + initial momentum of ball #2 (since ball #2 is stationary)
= 30 kg·m/s + 0 kg·m/s = 30 kg·m/s
2. According to conservation of momentum, the total momentum before the collision should be equal to the total momentum after the collision. Therefore, the total momentum of the system after the collision is also 30 kg·m/s.
3. Now, let's determine the final velocity of ball #1 after the collision. We know the mass of ball #1 is 6 kg, and its initial velocity is 2 m/s (moving forward). Therefore:
Final momentum of ball #1 = 6 kg × 2 m/s = 12 kg·m/s
4. Since the total momentum of the system after the collision is 30 kg·m/s, and we know the final momentum of ball #1, we can calculate the final momentum of ball #2:
Final momentum of ball #2 = Total final momentum - Final momentum of ball #1
= 30 kg·m/s - 12 kg·m/s = 18 kg·m/s
5. To determine the final velocity of ball #2, divide the final momentum of ball #2 by its mass (4 kg):
Final velocity of ball #2 = Final momentum of ball #2 / mass of ball #2
= 18 kg·m/s / 4 kg = 4.5 m/s
Since the initial velocity of ball #2 is 0 m/s (stationary), the final velocity of ball #2 is 4.5 m/s (moving in the same direction as ball #1).
6. The impulse of the system can be calculated by dividing the change in momentum by the time taken:
Impulse (J) = Change in momentum / Time
= (Final momentum - Initial momentum) / Time
= (30 kg·m/s - 0 kg·m/s) / 0.5 s
= 60 kg·m/s
Therefore, the impulse of the system is 60 kg·m/s.
7. Finally, to calculate the force exerted during the collision, divide the impulse by the time taken:
Force (F) = Impulse / Time
= 60 kg·m/s / 0.5 s
= 120 N
Hence, the force exerted during the collision is 120 Newtons.