Question

A 40 N force applied at an angle of 37 degrees above the horizontal pulls a 5kg
box on a horizontal floor. The
acceleration of the box is 3m/s2 . How large a fritional force must be retarding the motion of the box?

Answer 1

Answer on Question #51076 - Physics - Mechanics - Kinematics - Dynamics

A $F = 40\mathrm{N}$ force applied at an angle $\varphi$ of 37 degrees above the horizontal pulls a $m = 5\mathrm{kg}$ box on a horizontal floor. The acceleration of the box is $a = 3\frac{\mathrm{m}}{\mathrm{s}^2}$ . How large a frictional force $F_{f}$ must be retarding the motion of the box?

Solution:

According to the 2 Newton's law (horizontal plane) we obtain

$$m a = F \cos \varphi - F _ {f}$$

Or equivalently

$$F _ {f} = F \cos \varphi - m a = 4 0 \mathrm {N} \cdot \cos 3 7 {}^ {\circ} - 5 \mathrm {k g} \cdot 3 \frac {\mathrm {m}}{\mathrm {s} ^ {2}} \approx 1 7 \mathrm {N}$$

Answer: $F_{f} = F\cos \varphi - ma \approx 17N$ .

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