A 20.7 cm screwdriver is used to pry open a can of paint. If the axis of rotation is 2.25 cm from the
end of the screwdriver blade and a force of 29.3 N is exerted at the end of the screwdriver’s handle, what force is applied to the lid?
Answer in units of N
To solve this problem, we can use the concept of torque. Torque is calculated by multiplying the force applied perpendicular to the axis of rotation by the distance from the axis of rotation to the point where the force is applied.
Given:
Length of the screwdriver blade (L) = 20.7 cm = 0.207 m
Distance from the axis of rotation to the end of the screwdriver blade (r) = 2.25 cm = 0.0225 m
Force applied at the end of the screwdriver’s handle (F) = 29.3 N
First, we need to calculate the torque exerted by the force at the end of the handle.
Torque (τ) = Force (F) × Distance (r)
τ = 29.3 N × 0.0225 m
τ = 0.65925 N·m
Next, we need to calculate the torque exerted by the force applied to the lid. The torque exerted by the force applied to the lid should be equal to the torque exerted by the force at the end of the handle, as there is no rotational motion.
Torque (τ) = Force (F') × Distance (L - r)
0.65925 N·m = F' × (0.207 m - 0.0225 m)
Simplifying the equation:
0.65925 N·m = F' × 0.1845 m
Now, solve for F':
F' = 0.65925 N·m / 0.1845 m
F' ≈ 3.57425 N
Therefore, the force applied to the lid is approximately 3.57425 Newtons (N).
To find the force applied to the lid, we can use the principle of moments. The principle of moments states that the sum of the clockwise moments is equal to the sum of the counterclockwise moments.
In this scenario, the clockwise moment is created by the applied force at the end of the screwdriver's handle, and the counterclockwise moment is created by the force applied to the lid.
To calculate the moment, we need to consider the distance of each force from the axis of rotation.
Given:
Length of the screwdriver (L) = 20.7 cm = 0.207 m
Distance from the axis of rotation to the end of the screwdriver blade (A) = 2.25 cm = 0.0225 m
Force applied at the end of the screwdriver's handle (F1) = 29.3 N
To find the force applied to the lid (F2), we can use the moment equation:
Moment clockwise (F1) = Moment counterclockwise (F2)
F1 * A = F2 * B
Where B represents the distance from the axis of rotation to the lid.
Now, we need to find the value of B. Since the axis of rotation is 2.25 cm from the end of the screwdriver blade and the length of the screwdriver blade is 20.7 cm, we can subtract these two lengths to get the distance from the axis to the lid.
B = L - A
B = 0.207 m - 0.0225 m
B = 0.1845 m
Now we can substitute the given values into the moment equation to find the force applied to the lid:
29.3 N * 0.0225 m = F2 * 0.1845 m
Solving for F2:
F2 = (29.3 N * 0.0225 m) / 0.1845 m
F2 ≈ 3.577 N
Therefore, the force applied to the lid is approximately 3.577 N.
20.7-2.25=18.45 cm
Effort x Effort-arm = Load x Load-arm
Load is 18.45 29.3/2.25=…