Question

when a constant force is applied to an object, the acceleration of the object varies inversely with its mass. when a certain constant force acts upon an object with mass 6 kg, the acceleration of the object is 11 m/s². when the same force acts upon another object, its acceleration is 3 m/s². what is the mass of this object?

Explanation:

Step1: Use Newton's second - law $F = ma$

Since the force is constant, we have $F_1=F_2$. Let $m_1 = 6$ kg, $a_1=11$ m/s², $a_2 = 3$ m/s², and $m_2$ be the unknown mass. Then $m_1a_1=m_2a_2$.

Step2: Solve for $m_2$

We can rewrite the equation $m_1a_1=m_2a_2$ as $m_2=\frac{m_1a_1}{a_2}$. Substitute $m_1 = 6$ kg, $a_1 = 11$ m/s², and $a_2=3$ m/s² into the formula. So $m_2=\frac{6\times11}{3}$.

Step3: Calculate the value of $m_2$

$m_2=\frac{66}{3}=22$ kg.

Answer:

22