Consider a torque ⃗τ that is constant in both magnitude and direction, and acts on a rigid body of mass 10 kg at a point 1 m from the pivot.

How much work does the torque do on the rigid body, if it turns through an angle of 180◦ while the torque is acting? Assume the acceleration due to gravity is 10 m/s2.

To calculate the work done by the torque on the rigid body, we need to know the formula for work and understand how torque relates to work.

Work (W) is defined as the amount of energy transferred to or from an object by the application of a force over a displacement. Mathematically, it can be calculated using the formula: W = F * d * cos(θ), where F is the magnitude of the force, d is the displacement, and θ is the angle between the force vector and the displacement vector.

In this case, the torque (τ) is constant in both magnitude and direction. Torque is a measure of the turning force or rotational force applied to an object. The formula for torque is: τ = r * F * sin(θ), where r is the distance between the pivot point and the point of application of the force, F is the magnitude of the force, and θ is the angle between the force vector and the lever arm vector.

Given that the torque is constant in both magnitude and direction, we can imply that the force applied perpendicular to the lever arm is also constant. Therefore, the work done by the torque can be calculated as the product of the torque and the angle through which the rigid body turns.

In this case, the torque (τ) acts on a rigid body of mass 10 kg at a point 1 m from the pivot. The displacement (d) is given by the circumference of a circle with a radius of 1 m (since the rigid body turns through 180°). Therefore, d = 2πr = 2π * 1 m = 2π m.

Since the force and the displacement are perpendicular, the angle (θ) between the force vector and the displacement vector is 90°. Thus, cos(θ) = cos(90°) = 0.

Substituting the values into the work formula, we get: W = τ * d * cos(θ) = τ * (2π) * 0 = 0.

Therefore, the work done by the torque on the rigid body when it turns through an angle of 180° is 0.