Assume your file cabinet is sitting on a cart with wheels. It is sitting in
the middle of a room with a smooth floor. You want to move it against the
wall. You give it a push. It takes off, and before you know it, it slams into
the wall. It is hard to stop it, because it has linear
Linear momentum is a measure of an object's translational (as opposed to rotational) motion. The linear momentum p of an object is defined as the product of the object's mass m times its velocity v.
p = mv.
Linear momentum is a vector. Its direction is the direction of the velocity.
The Cartesian components of p are px = mvx, py = mvy, pz = mvz.
If an object's velocity is changing, its linear momentum is changing. For an object with constant mass we have
lim∆t-->0 ∆p/∆t = m lim∆t-->0 ∆v/∆t = m dv/dt = ma = F.
To change the linear momentum of an object of m, a net force has to act on it, causing the object to accelerate. F = dp/dt is a different way of stating Newton's second law. The rate at which an object's momentum changes is equal to the force acting on the object. If a force F acts on an object for a time ∆t, then the change in the object's momentum is ∆p = Favg∆t = ∫titf Fdt. If ∆t is a very short time interval, we say that the object receives an impulse I = ∆p = Favg∆t.
Note the difference:
Work: W = Favg·d (scalar)
Impulse: I = ∆p = Favg∆t (vector)
What is the magnitude of the momentum of a fly if it is traveling with speed 1 m/s and has a mass of 0.0001 kg?
A bullet is accelerated down the barrel of a gun by hot gases produced in the combustion of gun powder. What is the average force exerted on a 0.03 kg bullet to accelerate it to a speed of 600 m/s in a time of 2.00 ms (milliseconds)?
An object that has a small mass and an object that has a large mass have the same momentum p. Which object has the largest kinetic energy?
An object that has a small mass and an object that has a large mass have the same kinetic energy. Which mass has the largest magnitude of momentum p?
A car is stopped for a traffic signal. When the light turns green, the car
accelerates, increasing its speed from 0 to 5.2 m/s in 0.832s. What linear
impulse and average force does a 70 kg passenger in the car experience?
A 3 kg steel ball strikes a wall with a speed of 10.0 m/s at an angle of 60o with the surface. It bounces off with the same speed and angle. If the ball is in contact with the wall for 0.2 s, what is the average force exerted on the ball by the wall?
Does a large force always produce a larger impulse on a body than a smaller force does? Explain!