Question

a 5 kg blob of putty moving at 7 m/s slams into a 5 kg blob of putty at rest. calculate the speed of the two stuck - together blobs immediately after the collision.
a 0 m/s
b 35 m/s
c $\frac{35}{2}$ m/s
d $\frac{7}{2}$ m/s

Explanation:

Step1: Apply conservation of momentum

The initial momentum of the system is given by the momentum of the moving blob only since the other is at rest. The formula for momentum is $p = mv$. Let $m_1=m_2 = 5$ kg, $v_1=7$ m/s and $v_2 = 0$ m/s. The initial momentum $p_i=m_1v_1+m_2v_2=5\times7+5\times0 = 35$ kg·m/s. After the collision, the two blobs stick together, so $m_{total}=m_1 + m_2=5 + 5=10$ kg. Let the final velocity be $v_f$. By the law of conservation of momentum $p_i=p_f$, and $p_f=m_{total}v_f$.

Step2: Solve for final velocity

We know that $p_i = 35$ kg·m/s and $p_f=m_{total}v_f=(10)v_f$. Since $p_i = p_f$, we have $35=10v_f$. Solving for $v_f$, we get $v_f=\frac{35}{10}=\frac{7}{2}$ m/s.

Answer:

C. $\frac{7}{2}$ m/s