Physics 1: Impulse and Momentum

A crash test car of mass 1,000 kg moving at a constant speed of 12 m/s collides completely inelastically with an object of mass M at time t = 0. The ojbect was initally at rest. The speed v in m/s of the car object system after the collision is given as a function of time t in seconds by the expression

$v = \frac{8}{1 + 5t}$

A. Calculate the mass M of the object

B. Assuming an initial position of x = 0, determine an expression for the position of the car object system after the collision as a function of time t.

C. Determine an expression for the resisting force on the car object system after the collision as a function of time t.

D. Determine the impulse delivered to the car object system from t = 0 to t = 2.0 s.

In a laboratory experiment, you wish to determine the initial speed of a dart just after it leaves a dart gun. The dart of mass $m$ is fired with the gun very close to a wooden block of mass $M_0$ which hangs from a cord of length $l$ and negligible mass as shown below. Assume the size of the block is negligible compared to $l$ and the dart is moving horizontally when it hits the left side of the block at its center and becomes embedded in it. The block swings up to a maximum angle $\theta_{max}$ from the vertical. Express your answer to the following in terms of $m$ , $M_0$ , $l$ , $\theta_{max}$ , and $g$ .

C. The dart is now shot into a block of wood that is fixed in place. The block exerts a force F on the dart that is proportional to the dart's velocity v and in the opposite direction, that is F = -bv, where b is a constant. Derive an expression for the distance L that the dart penetrates into the block in terms of m, $v_0$ , and b.