Momentum of ball bouncing off crossbar

• luffy3san
In summary, a soccer ball with a mass of 416 g bounces off the crossbar of a goal and is deflected upward at an angle of 56.7° with respect to horizontal. Immediately after the deflection, the kinetic energy of the ball is 46.9 J. Using the equations for momentum and kinetic energy, the vertical and horizontal components of the ball's momentum are calculated to be 3.43 kg m/s and 5.22 kg m/s, respectively. Angular momentum is not considered in this problem.
luffy3san

Homework Statement

A soccer ball with a mass of 416 g bounces off the crossbar of a goal and is deflected upward at an angle of 56.7° with respect to horizontal. Immediately after the deflection, the kinetic energy of the ball is 46.9 J. What are the vertical and horizontal components of the ball's momentum immediately after striking the crossbar? (Let the horizontal direction be the x-direction and the vertical direction be the y-direction.)

P = mv
KE = 1/2mv2

The Attempt at a Solution

KEf = 0.5 * m * v2
46.9 = 0.5 * 0.416 * v2
v = 15 m/s

P = mv
Px = 0.416 kg * 15 m/s * cos 56.7 degrees = 3.43 kg m/s
Py = 0.416 kg * 15 m/s * sin 56.7 degrees = 5.22 kg m/s

Any help is appreciated. Thanks.

Last edited:
You should keep units everywhere, but I don't see where you need help.

mfb said:
You should keep units everywhere, but I don't see where you need help.

Ah sorry... I got those two values for the momentum, they were one of the options but was marked as wrong.

Last edited:
I get the same answers as you - assuming the ball's not spinning.

haruspex said:
I get the same answers as you - assuming the ball's not spinning.

Oh, thanks. We haven't covered angular momentum yet so shouldn't be... i think. I'll have to ask the instructor next class.

1. What is momentum?

Momentum is a physics concept that refers to the quantity of motion an object has. It is the product of an object's mass and its velocity.

2. How is momentum related to a ball bouncing off a crossbar?

When a ball bounces off a crossbar, its momentum changes. As the ball hits the crossbar, it experiences a force that causes it to stop momentarily and then change direction. This change in direction results in a change in momentum.

3. Does the mass of the ball affect its momentum when bouncing off a crossbar?

Yes, the mass of an object is a factor in determining its momentum. A heavier ball will have more momentum than a lighter ball when bouncing off a crossbar.

4. How does the velocity of the ball affect its momentum when bouncing off a crossbar?

The velocity of an object is directly proportional to its momentum. This means that the faster a ball is moving when it hits the crossbar, the greater its momentum will be.

5. Can the momentum of a ball bouncing off a crossbar be calculated?

Yes, the momentum of a ball bouncing off a crossbar can be calculated using the formula p = mv, where p is the momentum, m is the mass of the ball, and v is its velocity. However, this calculation may be affected by external factors such as air resistance and the elasticity of the ball and crossbar.

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