Question

the frame in (figure 1) supports the 550-lb load. the pulley at c has a radius of 0.5 ft . the pulley at d has a radius of 0.25 ft .

Answer 1

The pulley system requires a load of 1100 lbs to prevent rotation.

Step-by-step explanation:

Given that the pulley at point C has a radius of 0.5 ft and the pulley at point D has a radius of 0.25 ft, we can find the mechanical advantage of the pulley system. Mechanical advantage is the ratio of the output force to the input force. In this case, the output force is the load of 550 lbs and the input force is the force required to support the load without rotation.

To find the force required to prevent rotation, we can use the equation for torque:

Torque = Force * Radius

Since the force at point C and point D are equal due to the equilibrium of the system, we can write:

Torque at C = Torque at D

Force at C * Radius at C = Force at D * Radius at D

550 lbs * 0.5 ft = Force at D * 0.25 ft

Force at D = 550 lbs * 0.5 ft / 0.25 ft

Force at D = 1100 lbs

Therefore, a load of 1100 lbs must be placed on the cord to keep the pulley from rotating.

Answer 2

To determine the hanging mass that must be placed on the cord to keep the pulley from rotating, we need to consider the torque balance. The torque exerted by the hanging mass must be equal to the torque exerted by the frictionless plane. Setting these two torques equal and solving for the hanging mass will give us the answer.

Step-by-step explanation:

To determine the hanging mass that must be placed on the cord to keep the pulley from rotating, we need to consider the torque balance. The torque exerted by the hanging mass must be equal to the torque exerted by the frictionless plane. The torque exerted by the hanging mass is given by the product of the hanging mass and the radius of the pulley at point C, while the torque exerted by the frictionless plane is given by the product of the mass on the frictionless plane and the difference in the radii of the pulleys at point C and D. Setting these two torques equal and solving for the hanging mass will give us the answer.

Let's say the hanging mass is m kg. The torque exerted by the hanging mass is given by T = m * 9.8 * 0.5 ft. The torque exerted by the frictionless plane is given by T = (5.0 kg * 9.8 m/s^2 * (0.3 m - 0.2 m)) ft. Setting these two equal and solving for m will give us the answer.