3. A person exerts a force of 55 N on the end of a door 74 cm wide. What is the magnitude of the torque if the force is exerted a)perpendicular to the door b)at a 45 degree angle to the door, c) at a 125 degree angle to the door?

Torque= (F)sinTheta(r)

Given:
F=55N
d= 74cm (converted to M=0.74M)
Theta=90degrees.
Since,
Perpendicular is equal to 90 degrees, sin90 = 1.
T=55N(1)(0.74m)
Tperpendicular= 41N.

45degrees.
T=55(sin45)0.74
T=29N.

Hope this will help :)

a) Perpendicular to the door? That's one way to make sure the door doesn't budge! Well, the magnitude of the torque can be calculated by multiplying the force by the perpendicular distance from the line of action of the force to the axis of rotation. In this case, since the force is exerted perpendicular to the door, the perpendicular distance would be the width of the door (74 cm). So, the magnitude of the torque would be 55 N * 0.74 m = 40.7 Nm. Don't worry, this isn't a door slammer of a question!

b) Ah, a 45-degree angle? Now, we're getting a bit more creative! To find the magnitude of the torque, you would still multiply the force by the perpendicular distance. But since the force is now at a 45-degree angle, you'll need to find the component of the force that acts perpendicular to the door. You can do this by multiplying the force by the sine of the angle (45 degrees). Then, multiply that result by the distance (74 cm) to calculate the torque. Are you ready for it? It would be 55 N * sin(45 degrees) * 0.74 m = 36.8 Nm. Not too shabby!

c) A 125-degree angle? Now we're approaching a rather odd angle for door handling! But fear not, the process remains the same. Calculate the perpendicular distance by taking the width of the door (74 cm) and multiplying it by the sine of the angle (125 degrees). Then multiply the result by the force (55 N). The magnitude of the torque, in this case, would be 55 N * sin(125 degrees) * 0.74 m = 39.7 Nm. Just remember, this angle is a door-craze!

To calculate the torque exerted on a door, we need to know the force applied and the perpendicular distance from the axis of rotation to the line of action of the force.

a) If the force is perpendicular to the door:
In this case, the perpendicular distance is equal to half the width of the door since the force is applied at the end of the door.

Given:
Force (F) = 55 N
Width of the door (d) = 74 cm = 0.74 m

Perpendicular distance (r) = (0.74 m) / 2 = 0.37 m

To calculate torque (τ), we use the formula:
τ = F * r

τ = 55 N * 0.37 m
τ = 20.35 Nm

Therefore, the magnitude of the torque if the force is exerted perpendicular to the door is 20.35 Nm.

b) If the force is at a 45-degree angle to the door:
In this case, we need to find the resolved component of the force that acts perpendicular to the door. The magnitude of the resolved component will be F * cos(45°).

Given:
Angle (θ) = 45°

Resolving the force component:
Force component (Fc) = F * cos(θ)
Fc = 55 N * cos(45°) = 55 N * 0.7071 ≈ 38.79 N

Perpendicular distance remains the same (0.37 m)

To calculate torque (τ), we once again use the formula:
τ = F * r

τ = 38.79 N * 0.37 m
τ = 14.34 Nm

Therefore, the magnitude of the torque if the force is exerted at a 45-degree angle to the door is approximately 14.34 Nm.

c) If the force is at a 125-degree angle to the door:
Similar to the previous case, we need to find the resolved component of the force that acts perpendicular to the door. The magnitude of the resolved component will be F * cos(125°).

Given:
Angle (θ) = 125°

Resolving the force component:
Force component (Fc) = F * cos(θ)
Fc = 55 N * cos(125°) = 55 N * (-0.5736) ≈ -31.54 N

Perpendicular distance remains the same (0.37 m)

To calculate torque (τ), we once again use the formula:
τ = F * r

τ = -31.54 N * 0.37 m
τ ≈ -11.66 Nm

The negative sign indicates that the torque is in the opposite direction.

Therefore, the magnitude of the torque if the force is exerted at a 125-degree angle to the door is approximately 11.66 Nm.

To find the magnitude of the torque in each scenario, you need to consider two factors: the force applied and the lever arm.

The torque (τ) can be calculated using the equation:

τ = F * r * sin(θ)

where F is the applied force, r is the distance from the axis of rotation to the point of force application (lever arm), and θ is the angle between the force and the lever arm.

Let's calculate the torque in each scenario:

a) Perpendicular to the door:
In this case, the force is applied directly perpendicular to the door, so the angle between the force and the lever arm is 90 degrees. The given force is 55 N, and the lever arm is half the width of the door, which is 74 cm/2 = 37 cm = 0.37 m.

Using the equation, we have:
τ = 55 N * 0.37 m * sin(90°)
τ = 20.35 N·m

Therefore, the magnitude of the torque with the force applied perpendicular to the door is 20.35 N·m.

b) At a 45-degree angle to the door:
In this case, the force is applied at a 45-degree angle to the door. The given force of 55 N remains the same, but we need to calculate the new lever arm when the angle is 45 degrees. The lever arm can be found by multiplying the width of the door by the cosine of the angle (since the lever arm is the adjacent side of the angle).

The lever arm (r) = 74 cm * cos(45°) = 0.74 m * 0.7071 ≈ 0.5227 m

Using the equation, we have:
τ = 55 N * 0.5227 m * sin(45°)
τ ≈ 20.35 N·m

Therefore, the magnitude of the torque with the force applied at a 45-degree angle to the door is also approximately 20.35 N·m.

c) At a 125-degree angle to the door:
In this scenario, the force is applied at a 125-degree angle to the door. Similarly to the previous case, we keep the given force of 55 N and need to calculate the new lever arm, which, in this case, is the adjacent side of the angle.

The lever arm (r) = 74 cm * cos(125°) = 0.74 m * (-0.5736) ≈ -0.4206 m

Using the equation, we have:
τ = 55 N * (-0.4206 m) * sin(125°)
τ ≈ -17.45 N·m

Therefore, the magnitude of the torque with the force applied at a 125-degree angle to the door is approximately 17.45 N·m. Note that the negative sign indicates the direction of the torque is opposite to that of the positive direction.