Answer to Question #223192 in Physics for yang

Question

1.     a bullet of mass 300 g traveling horizontally towards the east with speed 300 m/s, which strikes a block of mass 1500 g that is initially at rest on a frictionless table. After striking the block, the bullet is embedded in the block and the block and the bullet move together as one unit. a. What is the magnitude and direction of the velocity of the block/bullet combination immediately after the impact? b. What is the magnitude and direction of the impulse by the block on the bullet? c. What is the magnitude and direction of the impulse from the bullet on the block? d. If it took 4 ms for the bullet to change the speed from 300 m/s to the final speed after impact, what is the average force between the block and the bullet during this time?

Answer 1

(a) Let's apply the law of conservation of momentum:

$$mv=(m+M)v_c,$$ $$v_c=\dfrac{mv}{(m+M)},$$ $$v_c=\dfrac{0.3\ kg\cdot300\ \dfrac{m}{s}}{(0.3\ kg+1.5\ kg)}=50\ \dfrac{m}{s}.$$

The sign plus means that the velocity of the block/bullet combination immediately after the impact directed eastward.

(b)

$$p=Mv_c=1.5\ kg\cdot50\ \dfrac{m}{s}=75\ N\cdot s.$$

The impulse by the block on the bullet directed toward the bullet.

(c)

$$p=Mv_c=1.5\ kg\cdot50\ \dfrac{m}{s}=75\ N\cdot s.$$

The impulse from the bullet on the block directed toward the block.

(d)

$$F_{avg}\Delta t=m|(v_f-v_i)|,$$ $$F_{avg}=\dfrac{m|(v_f-v_i)|}{\Delta t},$$ $$F_{avg}=\dfrac{0.3\ kg\cdot|(50\ \dfrac{m}{s}-300\ \dfrac{m}{s})|}{4\cdot10^{-3}\ s}=1.87\cdot10^4\ N.$$