Substituting the values of the mass, the velocity of the body The impulse on the body is, therefore, given by It has an average velocity in that time interval given by The question states a vertically downward displacement of the body of When the body moves in the water, the velocity of the body changes. The value of ? is the acceleration due to gravity on Earth,ĩ.8 m/s 2. The body is initially at rest, so ? is zero. Where ? is the initial vertical velocity of the body, The body when it reaches the water is given by We take here the downward direction as positive. We can therefore use the one-dimensional equations of motion involving the single components of these vectors.
In this question, the body moves in a straight line, which means that vector quantities such as forces, displacement, velocity, and acceleration are one-dimensional (along the motion axis). Find the magnitude of the change in its momentum as a result of the resistance of It reached the water’s surface afterĪs it moved through the water, it descended vertically with an average speed The following figure qualitatively illustratesĮxample 2: Finding the Change in the Momentum of a Body as a Result The impulse from the medium is applied to the body throughout the motion In its initial direction rather than making the body reverse. In the velocity of the body tending to some nonnegative minimum value In the opposite direction to the direction of its velocity but can only result The impulse from the resistive medium accelerates the body In momentum, which can be determined from the change in the velocity ofĪnother case of an impulse on a body is that of a body traveling in a Known to determine the impulse, as the impulse is equal to the change Was in contact with the barrier is not given and does not need to be It is worth noting that the time interval for which the sphere Momentum of the sphere equals the magnitude of the impulse on the sphere,
The direction of the impulse is opposite to the direction of the The impulse of the force is equal to the change in the momentum But as the direction of the sphere has reversed, the velocity now has k g m sĪfter rebounding, the component of the momentum of the sphere along the horizontal axis is given by ? = ? ?, where ? is the component of the velocity of the sphere along the horizontal axis after rebounding. The direction of the velocity of the sphere before rebounding is chosen toīe positive, giving an initial momentum for the sphere of Typically used for momentum, so the mass of the sphere is converted from Is ? = ? ?, where ? is the component of the velocity of the body along the horizontal axis before it hit the wall. Since the sphere is moving in a horizontal line, the component of the momentum along the horizontal axis, ? , The change in the momentum can be determinedįrom the momentum of the sphere before and after it rebounds.īefore rebounding, the momentum of the sphere is given by The impulse of the force that acts on the sphere as it rebounds changes Determine the magnitude of the impulse exerted on the sphere. When it hit a smooth vertical wall and rebounded atĩ m/s. Was moving horizontally in a straight line at Integrating both sides of the equation over the time interval gives ? ? = ? ? ? ? = ? = ? − ? ? = Δ ? ? = ? ( ? − ? ), d d d d where ? = ? ( ? ) is the velocity of the body before the force acts on it and ? = ? ( ? ) is the velocity of the body when the force has stopped acting on it.Įxample 1: Finding the Impulse Exerted on a Sphere Moving on a Horizontal Smooth d dĪnd as ? = ? ? and ? is constant, the above relation can be written as ? = ? ?. When a net force, ⃑ ?, acts on a body of constant mass, ?, according to Newton’s second law of motion, the body’s acceleration is proportional to the force and inversely proportional to the mass, as expressed by the formula ? = ? ?, or ? = ? ?, where ⃑ ? is the acceleration of the body. We see that the momentum of a body is proportional to both its mass and its velocity.įurthermore, the momentum of a body is a vector quantity that has the same direction as the body’s velocity. The momentum of a body is given by ? = ? ?, where ? is the mass of the body and ⃑ ? is the velocity of the body.