Answer:
(a) 10N
Explanation:
The sketch of the two cases has been attached to this response.
Case 1: The box is pushed by a horizontal force F making it to move with constant velocity.
In this case, a frictional force [tex]F_{r}[/tex] is opposing the movement of the box. As shown in the diagram, it can be deduced from Newton's law of motion that;
∑F = ma -------------------(i)
Where;
∑F = effective force acting on the object (box)
m = mass of the object
a = acceleration of the object
∑F = F - [tex]F_{r}[/tex]
m = 50kg
a = 0 [At constant velocity, acceleration is zero]
Substitute these values into equation (i) as follows;
F - [tex]F_{r}[/tex] = m x a
F - [tex]F_{r}[/tex] = 50 x 0
F - [tex]F_{r}[/tex] = 0
F = [tex]F_{r}[/tex] -------------------(ii)
Case 2: The box is pushed by a horizontal force 1.5F making it to move with a constant velocity of 0.1m/s²
In this case, the same frictional force [tex]F_{r}[/tex] is opposing the movement of the box.
∑F = 1.5F - [tex]F_{r}[/tex]
m = 50kg
a = 0.1m/s²
Substitute these values into equation (i) as follows;
1.5F - [tex]F_{r}[/tex] = m x a
1.5F - [tex]F_{r}[/tex] = 50 x 0.1
1.5F - [tex]F_{r}[/tex] = 5 ---------------------(iii)
Substitute [tex]F_{r}[/tex] = F from equation (ii) into equation (iii) as follows;
1.5F - F = 5
0.5F = 5
F = 5 / 0.5
F = 10N
Therefore, the value of F is 10N
