Concept explainers
The force required to just tip the box.
Answer to Problem 96A
The force required to just tip the box is
Explanation of Solution
Given:
The distance of rope from the rope is
The width of the box is
The height of the box is
The coefficient of friction is
Formula used:
The torque is the product of the lever arm and the applied force. The expression for the torque is,
Here,
Calculation:
Consider a line that passes through centre of mass of box. Also, it is perpendicular to the box’s surface that is considered as the axis of rotation.
Consider the distance between the centre and bottom of the box be
The free body diagram of the box is shown below.
The value of the distance
The frictional force acting between the box surface and the floor is denoted by
The weight of the box, whose mass is M , is
The torque
Consider the force applied on the rope as
The torque
For rotational equilibrium of the box,
Substitute the values in the above equation,
The denominator of the equation will be zero when the box is pulled at the height of center of mass. This means that box can be pulled with any amount of force and it will not tip the box.
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