Question

PLLLLLLLLLZ HELP 30 POINTS ANSWER ONLY IF YOU KNOW

Answer 1

Answer:

The resulting acceleration of the box is 3.92 $m/s^2$

Explanation:

Please refer to the Free Body Diagram

According to the second Newton's Law, the acceleration of the mass will depend on the net force applied to it.  

In the y-axis, the net force is zero since the mass won't move in that direction. We only need to analyze the dynamics on the x-axis.

The problem states that initially, the box moves at a constant speed which means zero acceleration, or zero net force.

If we analyze the forces on the x-axis we find:

F - Fr = m.a

Where F is the originally applied force, Fr is the Friction force, m is the mass of the box and a is the initial acceleration, which we found to be zero. Thus:

F - Fr = 0 => F = Fr = $\mu$.N, being N the Normal force and $\mu$ the kinetic friction coefficient

By analyzing the y-axis, we find N = W = m.g

So N = 50 kg. 9.8 $m/s^2$ = 490 Nw

The Friction force is then:

Fr = 490 Nw . 0.2 = 98 Nw

Which gives us the initial Force:

F = 98 Nw

When tripled, the new Force will be

F' = 294 Nw

And the corresponding x-axis equilibrium condition is:

F' - Fr = m.a'  ....(a' is the resulting acceleration). So we have:

$a=\frac{F'-Fr}{m}=\frac{294Nw-98Nw}{50 Kg} =\frac{196Nw}{50Kg}$

a = 3.92 $m/s^2$