Question Video: Finding the Impulse of the Collision of Two Spheres, One Moving on the Horizontal Plane and the Other Resting on the Same Plane Mathematics

A sphere of mass 675 g was moving in a straight line on a smooth horizontal table at 31 cm/s. The sphere crashed into another sphere of mass 837 g that was at rest on the table. If the first sphere came to rest as a result of the impact, find the magnitude of the impulse between the two spheres.

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Video Transcript

A sphere of mass 675 grams was moving in a straight line on a smooth horizontal table at 31 centimeters per second. The sphere crashed into another sphere of mass 837 grams that was at rest on the table. If the first sphere came to rest as a result of the impact, find the magnitude of the impulse between the two spheres.

When dealing with any collisions question of this type, it is worth drawing a before-and-after diagram. The first sphere has a mass of 675 grams. The second sphere has a mass of 837 grams. We are told that, prior to the collision, the first sphere is moving at a speed of 31 centimeters per second, whereas the second sphere is at rest. After the collision, the first sphere comes to rest, and the speed of the second sphere is unknown. We are asked to calculate the magnitude of the impulse between the two spheres, and we know that impulse is the change in momentum. This can be calculated using the formula 𝐼 equals 𝑚𝑣 minus 𝑚𝑢.

We know that momentum is equal to mass multiplied by velocity. Therefore, 𝑚𝑢 is equal to the momentum before the collision and 𝑚𝑣 is equal to the momentum after the collision. By factoring out the mass, we can rewrite the impulse equation as 𝑚 multiplied by 𝑣 minus 𝑢. We can now calculate the impulse on the first sphere. The mass is equal to 675 grams. The velocity after the collision was zero centimeters per second, and the velocity before the collision was 31 centimeters per second. We need to multiply 675 by negative 31. This is equal to negative 20,925. However, we wish to calculate the magnitude of the impulse. As the magnitude is always positive, this is equal to 20,925.

It is common to measure impulse in newton seconds as we are often given the mass in kilograms and the speed in meters per second. In this question, however, the mass was given in grams and the speed in centimeters per second. When this is true, our units for impulse will be dyne seconds. The magnitude of the impulse between the two spheres is 20,925 dyne seconds.

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