Question

work each of the following problems. show all work.

1. a spring is compressed between two blocks, one with a mass of 2 kg and the other with a mass of 3 kg. if the 2 kg block has an average acceleration of 6 m/s² when the spring acts on it, what will be the average acceleration of the 3 kg block?
2. a 30 kg girl and a 40 kg boy stand on rollerskates, face one another, and push off each other. if the boy accelerates backward with an acceleration of 6 m/s², what will be the acceleration of the girl?
3. a 1000 kg car collides with a 1 mg mosquito. by what factor will the acceleration of the mosquito be greater than the acceleration of the car when they collide?

Explanation:

Step1: Find the force on the 2 kg block

According to Newton's second law \(F = ma\). For the \(2\) kg block, \(m_1=2\) kg and \(a_1 = 6\) m/s². So \(F_1=m_1a_1\).
\(F_1=2\times6 = 12\) N.

Step2: Use the fact that the force on both blocks is the same (Newton's third law)

The force on the \(3\) kg block \(F_2=F_1 = 12\) N.

Step3: Calculate the acceleration of the 3 kg block

Again, using Newton's second law \(a=\frac{F}{m}\). For the \(3\) kg block, \(m_2 = 3\) kg and \(F_2=12\) N. So \(a_2=\frac{F_2}{m_2}\).
\(a_2=\frac{12}{3}=4\) m/s².

Answer:

The average acceleration of the \(3\) kg block is \(4\) m/s².