Question

A mass m = 1 kg is falling downward under the effect of gravity and of a vertical upward force P = 3 N. Assuming for simplicity that g≅10 m/s2. What is the acceleration of the mass?
A: 7 m/s2 upward
B: 3.5 m/s2 downward
C: 10 m/s2 downward
D: 7 m/s2 downward
E: 3 m/s2 upward

Answer 1

Answer on Question #77746, Physics / Mechanics | Relativity

A mass $m = 1$ kg is falling downward under the effect of gravity and of a vertical upward force $P = 3$ N. Assuming for simplicity that $g \cong 10 \, \text{m/s}^2$. What is the acceleration of the mass?

A: $7 \, \text{m/s}^2$ upward

B: $3.5 \, \text{m/s}^2$ downward

C: $10 \, \text{m/s}^2$ downward

D: $7 \, \text{m/s}^2$ downward

E: $3 \, \text{m/s}^2$ upward

Solution

$$m = 1 \, \text{kg}$$ $$P = 3 \, \text{N}$$ $$g = 10 \, \text{m/s}^2$$

a-?

Free body diagram

Newton’s Second Law of motion: $\overrightarrow{F_{net}} = m\vec{a}$

$$\overrightarrow{F_{grav}} + \vec{P} = m\vec{a}$$ $$m\vec{g} + \vec{P} = m\vec{a}$$ $$y: -mg_y + P_y = m a_y$$ $$-1 \times 10 + 3 = 1 \times a_y$$ $$a_y = -7 \, (\text{m/s}^2)$$

As $a_y$ is negative it’s direction is opposite to $y$ axis, consequently the body A moves downward with the acceleration of mass $7 \, \text{m/s}^2$

Answer: D: $7 \, \text{m/s}^2$ downward

Answer provided by https://www.AssignmentExpert.com