Question

Determine the net torque on the 2.6-m-long uniform beam shown in the figure. All forces are shown. (Figure 1) Figure 1 of 1 56 N 65 N 45° 52 N ▼ Calculate about point C, the CM. Take counterclockwise torques to be positive. Express your answer using two significant figures. D [-] ΑΣΦ ? Tabout C = m. N Submit Previous Answers Request Answer X Incorrect; Try Again; 28 attempts remaining Part B Calculate about point point P at one end. Take counterclockwise torques to be positive. Express your answer using two significant figures. IVE| ΑΣΦ ? Tabout P = m. N Submit Request Answer

Answer 1

Net torque is calculated by summing up individual torques from all applied forces, which is the product of each force, the distance from the pivot point, and the sine of the angle between the force and lever arm. The center of mass simplifies torque calculations when used as the pivot. Counterclockwise torques are positive, and clockwise torques are negative.

Step-by-step explanation:

To calculate the net torque on a beam, you need to consider each force's contribution to the rotational motion around a pivot point. When examining torques around, for instance, the center of mass (CM) of a beam, you apply the concept of torque (τ), which is the product of the force (F), the distance (lever arm, r) from the pivot point to the point where the force is applied, and the sine of the angle (θ) between the force and the lever arm. The formula for torque is τ = F × r × sin(θ). The counterclockwise torque is considered positive, and the clockwise torque is negative. Additionally, the net torque is the sum of all individual torques.

In a situation with multiple forces, like on a flywheel or a beam with weights, you treat each force separately, calculate its torque, and then sum them, taking into account their directions to determine the overall net torque. In the case of a beam, if it has uniform mass distribution, the center of mass is typically at its midpoint, which simplifies the torque calculations when using it as the pivot point. Remember that when a force is directly perpendicular to the lever arm, the angle is 90°, and the sine of 90° is 1, making the torque calculation a straightforward multiplication of force and distance.

Answer 2

Calculating net torque involves summing the individual torques produced by each force, using the perpendicular distance from the pivot point to the force's line of action, the force's magnitude, and the angle of the force with respect to the pivot point.

Step-by-step explanation:

To calculate the net torque exerted on a beam (or any rigid body), you must consider the individual torques produced by each force acting on the body. The torque (τ) caused by each force can be calculated using the equation τ = rFsin(θ), where r is the perpendicular distance from the pivot point to the line of action of the force, F is the magnitude of the force, and θ is the angle between the force and a line drawn from the pivot point to the point where the force is applied.

To assess torque about point C, the center of mass (CM) of the beam, you calculate the torque produced by each force and then sum them, taking into account their directions (clockwise or counterclockwise). Similarly, to compute the torque about point P, which is one end of the beam, you apply the same process considering point P as the pivot point.