Impulse and Momentum (finding net force)

In summary: In this scenario, a 0.500-kg ball is dropped from rest at a height of 1.20 m and rebounds to a height of 0.700 m. The change in momentum of the ball can be determined by calculating its speed before and after the impact with the floor. The magnitude and direction of the impulse of the net force applied to the ball during the collision can then be determined using this change in momentum. The issue of getting an incorrect result may be due to errors in using the potential and kinetic energy equations. More guidance is needed to accurately solve this problem. In summary, it is important to calculate the ball's change in momentum to determine the magnitude
  • #1
acra
1
0
A 0.500-kg ball is dropped from rest at a point 1.20 m above the floor. The ball reboundes straight upward to a height of 0.700 m. What are the magnitude and direction of the impulse of the net force applied to the ball during the collision with the floor?

I have been trying to solve this various ways, I have tried using PE and KE, but I keep on coming up with 3.1305 instead of the 4.28 which I should be getting.

Any guidance would be greatly appreciated.
 
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  • #2
acra said:
A 0.500-kg ball is dropped from rest at a point 1.20 m above the floor. The ball reboundes straight upward to a height of 0.700 m. What are the magnitude and direction of the impulse of the net force applied to the ball during the collision with the floor?

I have been trying to solve this various ways, I have tried using PE and KE, but I keep on coming up with 3.1305 instead of the 4.28 which I should be getting.

Any guidance would be greatly appreciated.
You have to determine the ball's change in momentum. To do that you need to know its speed immediately before and immediately after the impact with the floor.

Can you determine these speeds from the two heights given?

AM
 
  • #3


The impulse-momentum theorem states that the change in momentum of an object is equal to the net force applied to the object multiplied by the time interval over which it acts. In this case, we can use this theorem to find the magnitude and direction of the impulse of the net force applied to the ball during the collision with the floor.

First, we need to calculate the initial and final momentum of the ball. The ball is initially at rest, so its initial momentum is zero. When it rebounds, it will have a final velocity v, which we can calculate using the equation v^2 = u^2 + 2as, where u is the initial velocity (zero), a is the acceleration due to gravity (9.8 m/s^2), and s is the displacement (1.20 m). Solving for v, we get v = 4.38 m/s.

The final momentum of the ball can be calculated using the equation p = mv, where m is the mass of the ball (0.500 kg) and v is the final velocity (4.38 m/s). Therefore, the final momentum of the ball is 2.19 kg*m/s.

Using the impulse-momentum theorem, we can now calculate the net force applied to the ball during the collision with the floor. The change in momentum is equal to the final momentum minus the initial momentum, so we have:

Δp = 2.19 kg*m/s - 0 kg*m/s = 2.19 kg*m/s

The time interval over which this change in momentum occurs is the time it takes for the ball to go from its initial position to its final position, which is the time it takes to fall from a height of 1.20 m and then rebound back to a height of 0.700 m. This can be calculated using the equation t = √(2s/g), where s is the displacement (1.20 m) and g is the acceleration due to gravity (9.8 m/s^2). Solving for t, we get t = 0.439 s.

Now, we can calculate the magnitude of the net force applied to the ball during the collision using the equation F = Δp/t. Plugging in our values, we get:

F = 2.19 kg*m/s / 0.439 s = 4.99 N

Therefore, the magnitude of the impulse of the net force applied to
 

Related to Impulse and Momentum (finding net force)

1. What is the difference between impulse and momentum?

Impulse and momentum are both physical quantities that describe the motion of an object. However, impulse refers to the change in an object's momentum over a period of time, while momentum is a measure of an object's motion and is equal to the product of its mass and velocity.

2. How do you calculate impulse?

Impulse can be calculated by multiplying the force applied to an object by the time over which it acts. Mathematically, it can be represented as J = FΔt, where J is impulse, F is force, and Δt is the change in time.

3. What is the equation for momentum?

The equation for momentum is p = mv, where p is momentum, m is mass, and v is velocity. This equation states that momentum is directly proportional to an object's mass and velocity.

4. How do you find the net force using impulse and momentum?

To find the net force using impulse and momentum, you can use the equation F = Δp/Δt, where F is net force, Δp is the change in momentum, and Δt is the change in time. This equation states that the net force acting on an object is equal to the change in its momentum over the change in time.

5. What are some real-life applications of impulse and momentum?

Impulse and momentum are important concepts in many real-life situations, such as car crashes, collisions in sports, and rocket propulsion. They are also used in engineering to design structures and machines that can withstand or utilize large forces and impacts.

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