Systems of Particles & Linear Momentum

A constant force of 20 N is applied to an object for 2 seconds. What is the impulse on the object?

Under what conditions is linear momentum conserved in a system?

A 2.0 kg block moving at 5.0 m/s on a frictionless surface collides with a 3.0 kg block at rest. After the collision, the 2.0 kg block moves at 1.0 m/s at an angle of 30 degrees relative to its original direction, and the 3.0 kg block moves at an angle of -45 degrees. What is the approximate speed of the 3.0 kg block?

A non-uniform rod of length $L$ has a linear mass density given by $\lambda(x) = Ax$, where $A$ is a constant and $x$ is the distance from one end. Determine the x-coordinate of the center of mass.

What is impulse?

A 2 kg object moving at 3 m/s collides head-on with a 1 kg object at rest. If the collision is perfectly inelastic, what is the final velocity of the combined mass?

What is the significance of the center of mass (COM) in analyzing the motion of a system of particles?

Two particles with masses $m_1 = 2 \text{ kg}$ and $m_2 = 4 \text{ kg}$ are located at positions $x_1 = 1 \text{ m}$ and $x_2 = 7 \text{ m}$ along the x-axis, respectively. What is the x-coordinate of the center of mass of this system?

A variable force is applied to an object. The force is described by the function $F(t) = 3t^2 + 2t$, where $F$ is in Newtons and $t$ is in seconds. What is the impulse on the object from $t = 0$ to $t = 2$ seconds?