Question

Two ropes are attached to a 35 kg object. The first rope applies a force of 20 N and the second applies a force of 55 N. If the two ropes are perpendicular to each other, what is the resultant acceleration of the object?

Answer 1

Answer:

Explanation:

mass of the object, m = 35 kg

Force in one direction, F1 = 20 N

force in perpendicular direction, F2 = 55 N

The net force is given by

$F=\sqrt{F_{1}^{2}+F_{2}^{2}}$

$F=\sqrt{20^{2}+55^{2}}$

F = 58.5 N

Let a be the net acceleration.

By the newton's second law

F = m a

58.5 = 35 x a

a = 1.67 m/s²

Answer 2

Answer:

$a=1.672\ m.s^{-2}$

Explanation:

Given:

• mass of the object, $m=35\ kg$

forces by two mutually perpendicular ropes of the attached to the object:

• $F_x=20\ N$

• $F_y=55\ N$

Now we find the resultant force effect due to the two given forces:

$F=\sqrt{F_x^2+F_y^2}$

$F=\sqrt{(20)^2+(55)^2}$

$F=58.52\ N$

Now the acceleration will be due to this resultant force:

$a=\frac{F}{m}$

$a=\frac{58.52}{35}$

$a=1.672\ m.s^{-2}$