Question

Forces of 8.85 N and 2.21 N act at right angles on a stack. What is the mass of the stack if it accelerates at a rate of 4.4 m/s^2?

Answer 1

Forces of 8.85 N and 2.21 N act at right angles on a stack. What is the mass of the stack if it accelerates at a rate of $4.4 \, \text{m/s}^2$ ?

Solution:

$\mathrm{F}_1 = 8.85 \mathrm{~N} -$ first force;

$\mathrm{F}_2 = 2.21 \mathrm{~N} -$ second force;

$a = 4.4 \frac{\mathrm{m}}{\mathrm{s}^2} -$ acceleration of the stack;

The resultant force $F$ of the triangle ABC:

$$\vec {F} = \vec {F} _ {1} + \vec {F} _ {2}; \left| \vec {F} \right| = \sqrt {\left| \vec {F} _ {1} \right| ^ {2} + \left| \vec {F} _ {2} \right| ^ {2}}$$ $$F = \sqrt {F _ {1} ^ {2} + F _ {2} ^ {2}}$$

Newton's second law for the stack:

$$\vec {\mathrm {F}} = \mathrm {m} \vec {\mathrm {a}}$$ $$x: F = m a$$ $$m = \frac {F}{a}$$

(1)in(2):

$$m = \frac {F}{a} = \frac {\sqrt {F _ {1} ^ {2} + F _ {2} ^ {2}}}{a} = \frac {\sqrt {(8 . 8 5 N) ^ {2} + (2 . 2 1 N) ^ {2}}}{4 . 4 \frac {m}{s ^ {2}}} = 2. 0 7 k g$$

Answer: mass of the stack is $2.07\mathrm{kg}$