1. A gate is hinged at A and B. Rope CD is tightened so that the net force in the x is zero. Given that AD=1.5m, AB=2m, BC=2.5m, Force of gravity= 595N
a. What is the tension in rope CD
b. What is the horizontal force at rope B
c. What is the combined vertical force at A and B
2. A mosquito is traveling at 5m/s and weighs 2kg. What is the net force?
a. Same mosquito is traveling at 5 m/s in a circle of radius 3m. What is the new net force?
3. A solid cylinder and a hollow cylinder are released from mass down a ramp. Which one reaches the bottom first? No math just explain: solid
Which has a higher final kinetic energy? No math just explain: same final kinetic energy
- the solid?
To answer these questions, we can use the principles of Newton's laws of motion. Here's how you can find the answers to each question:
1.
a. To find the tension in rope CD, we need to consider the forces acting on the gate. Since the net force in the x-axis is zero, the only forces present are the tension in rope CD and the gravitational force acting at point A. Since the gate is in equilibrium, the tension in rope CD must be equal to the gravitational force at point A. Therefore, the tension in rope CD is 595N.
b. To find the horizontal force at rope B, we need to consider the forces acting at point B. The horizontal force at point B is the horizontal component of the tension in rope CD, which can be found using trigonometry. We can use the cosine rule to determine the angle between the rope CD and the x-axis. Then, we can use this angle to calculate the horizontal force at rope B.
c. To find the combined vertical force at points A and B, we need to consider the vertical forces acting on the gate. The only vertical force acting is the weight of the gate, which is the force of gravity. The combined vertical force at points A and B is equal to the weight of the gate, which is 595N.
2.
a. The net force on the mosquito can be calculated using the equation F = m * a, where F is the net force, m is the mass of the mosquito, and a is its acceleration. Since the mosquito is traveling at a constant velocity of 5m/s, its acceleration is zero. Therefore, the net force on the mosquito is also zero.
b. When the same mosquito is traveling at 5 m/s in a circle of radius 3m, it is undergoing circular motion. In circular motion, there is a centripetal force directed towards the center of the circle. The magnitude of this centripetal force can be calculated using the equation F_c = m * (v^2 / r), where F_c is the centripetal force, m is the mass of the mosquito, v is its velocity, and r is the radius of the circular path. Therefore, to find the new net force, you need to calculate the centripetal force.
3. The solid cylinder will reach the bottom of the ramp first. This is because the solid cylinder has more mass compared to the hollow cylinder of the same size. As they slide down the ramp, both cylinders experience the same gravitational force, but the solid cylinder has more mass, meaning it has stronger inertia. As a result, it will take longer for the hollow cylinder to overcome its inertia and reach the bottom.
Both cylinders will have the same final kinetic energy at the bottom of the ramp. The final kinetic energy only depends on the final velocity of the objects, which is determined by the height of the ramp and their initial potential energy. Since both cylinders start at the same height on the ramp, they will have the same potential energy and will reach the same final velocity at the bottom. Therefore, they will have the same final kinetic energy.