An object of mass m is thrown vertically upwards.At what rate will its momentum change?
To determine the rate at which the momentum of an object changes, we need to consider the forces acting on it and apply Newton's second law of motion. In this case, the only significant force acting on the object is gravity.
When the object is thrown vertically upwards, gravity acts in the opposite direction to the velocity. As a result, the net force on the object is given by the equation:
F(net) = -mg,
where "m" represents the mass of the object and "g" is the acceleration due to gravity.
Using Newton's second law, we can relate the net force to the rate of change of momentum:
F(net) = dp/dt,
where "dp" represents the change in momentum and "dt" is the change in time.
By equating these two equations, we have:
-dp/dt = mg.
Rearranging, we find:
dp = -mg dt.
Integrating both sides of the equation gives:
Δp = -mg Δt.
Therefore, the rate at which the momentum changes can be expressed as the negative product of mass, acceleration due to gravity, and the change in time.