Question

An applied force of 200.0N gives a sled a acceleration of 2.00m/s^2. If you place an additional 60kg mass on the sled, what will the acceleration be?

Answer 1

Answer on Question #39802, Physics, Mechanics | Kinematics | Dynamics

Question:

An applied force of 200.0N gives a sled an acceleration of $2.00\mathrm{m/s^2}$. If you place an additional 60kg mass on the sled, what will the acceleration be?

Answer:

Newton's second law of motion can be expressed in equation form as follows:

$$\sum \vec{F} = m \vec{a}$$

Therefore:

$$F = m_s a_0$$

where $m_s$ is mass of sled, $a_0$ is initial acceleration

With additional mass:

$$F = (m_s + m) a$$

From first equation:

$$m_s = \frac{F}{a_0}$$

And from second:

$$a = \frac{F}{m_s + m} = \frac{F}{\frac{F}{a_0} + m} = \frac{a_0}{1 + \frac{m a_0}{F}} = \frac{2}{1 + \frac{60 \cdot 2}{200}} = 1.25 \frac{m}{s}$$

Answer: $1.25 \frac{m}{s}$