Question

A 23 cm screwdriver is used to pry open a can of paint . If the axis of rotation is 2 cm from the end of a screwdriver blade and a force of 83.4N is exerted at the end of the screwdriver’s handle ,what force is applied to the lid?

Answer 1

The rotational equilibrium condition allows to find the result for the value of the force on the lid is:

• The force on the lid is: F₂ = 875.7 N

Rotational equilibrium condition.

The torque of a force is defined by the cross product of the force times the distance from the point of application.

             τ = F x r

where bold indicates vectors, tau is torque, F is force, and r is displacement.

Newton's second law for rotational motion establishes a relationship between the net torque, the moment of inertia, and the angular acceleration of the body, in the special case that the angular acceleration is zero, is called the rotational equilibrium condition.

             Σ τ = 0

In the attachment we can see a diagram of the forces in this system, we assume that the lid does not move, so we can use the rotational equilibrium condition, where we will assume that the counterclockwise rotations are positive.

             

They indicate the force F = 83.4 N su and the pivot point is l = 2 cm from the length of the screwdriver L = 23 cm.

The distance from the force to the pivot point is:

           r₁ = L - l

           r₁ = 23-2 = 21cm

Let us write the condition of rotational equilibrium.

          F₁ r₁ + F₂ l = 0

           $F_2 = - \frac{r1}{l} \ F_1$

Let's calculate.

            F₂ = -$- \frac{21}{2}\ 83.4$

            F₂ = -875.7 N

The negative sign indicates that the force is in the opposite direction to the applied force.

In conclusion using the rotational equilibrium condition we can find the result for the value of the force on the lid is:

• The force on the lid is: F2 = 875.7 N

Learn more about rotational equilibrium condition here:  brainly.com/question/18117041

Answer 2

The force applied to the lid with the screwdriver is 875.7 N.

The given parameters:

• Length of the screwdriver, L = 23 cm
• Radius of the rotation, r = 2 cm
• Applied force, F = 83.4 N

What is principle of moment?

The principle of moment states that the sum of clockwise moment is equal to sum of anticlockwise moment.

The sketch of the given question

----------2cm----------------------------------- 23cm

↓           Δ                                           ↓

F                                                          83.4 N

Take moment about the pivot as follows;

anticlockwise moment = clockwise moment

F(2cm) = 83.4(23cm - 2 cm)

$F(2cm) = 83.4N(21cm)\\\\F = \frac{83.4N(21cm)}{2cm} \\\\F = 875.7 \ N$

Thus, the force applied to the lid with the screwdriver is 875.7 N.

Learn more about principle of moment here: brainly.com/question/20298772