Question

a man pulls a suitcase of mass 10.4 kt with the force of 25N inclined to the horizontal at an angle of 30°. as a result the suitcase accelerates horizontally. what is the magnitude of acceleration?

Answer 1

Given:

A man pulls a suitcase of mass 10.4 kt with the force of 25N inclined to the horizontal at an angle of 30°. as a result the suitcase accelerates horizontally.

To find:

Magnitude of acceleration ?

Calculation:

Since the force has been applied at an angle, the component of the force along the horizontal plane will be responsible for movement of the object.

• Mass = 10 kt = 10 × 10³ t = 10⁴ × 10³ kg = 10⁷ kg.

$\therefore \: \sf \: a_{h} = a \times \cos( \theta)$

$\implies \: \sf \: a_{h} = \dfrac{force}{mass} \times \cos( \theta)$

$\implies \: \sf \: a_{h} = \dfrac{25}{(10 \times {10}^{3}) \times {10}^{3} } \times \cos( {30}^{ \circ} )$

$\implies \: \sf \: a_{h} = \dfrac{25}{ {10}^{7} } \times \cos( {30}^{ \circ} )$

$\implies \: \sf \: a_{h} = \dfrac{25}{ {10}^{7} } \times \dfrac{ \sqrt{3} }{2}$

$\implies \: \sf \: a_{h} = 21.65 \times {10}^{ - 7} \: m/ {s}^{2}$

So horizantal acceleration is 21.65 × 10^(-7) m/s².