Forces 2 Questions PLEASE HELP

[anakinmalta]

Homework Statement

1. A car tows a van of mass 1000kg with uniform speed of 10m/s. The tension in the coupling is 500N. Explain why the thension is not zero. The car now accelerates at 2m/s^2. What is the new tension in the coupling?


2. A crane is to haul a mass of 1000kg onto a deck of a ship. Find the tension in the cable when the load is A Held at rest off the ground. B Raised with an acceleration of 0.5m/s^2 C Raised with uniform speed of 1.5 m/s D Lowered with an acceleration of 1m/s^2. E Brought to rest while being lowered at 0.4 m/s^2

The Attempt at a Solution

dunno

 

[HallsofIvy]

That's unfotunate! Do you have no idea why there should be tension in a coupling even if there is no acceleration? What would happen to the trailer if the trailer hitch gave way? Why?

For the rest, surely you know that "force equal mass times acceleration"!

 

[ogb p]

1. The tension in the coupling is not zero because of Newton's Second Law of Motion, which states that an object will remain at rest or continue at a constant velocity unless acted upon by a net external force. In this scenario, the car is pulling the van with a constant speed of 10m/s, which means there must be a force acting on the van to counteract the friction and air resistance that would naturally slow it down. The tension in the coupling is this external force that is keeping the van moving at a constant speed.

When the car accelerates at 2m/s^2, the tension in the coupling will increase. This is because the acceleration of the car will also cause an acceleration of the van, and to maintain a constant distance between the two vehicles, the tension in the coupling must increase to keep the van from falling behind.

2. a) When the load is held at rest off the ground, the tension in the cable will be equal to the weight of the load, which is 1000kg multiplied by the acceleration due to gravity, 9.8m/s^2. Therefore, the tension will be 9800N.

b) When the load is raised with an acceleration of 0.5m/s^2, the tension in the cable will be equal to the sum of the weight of the load and the force required to accelerate it. This can be calculated using Newton's Second Law of Motion: F=ma, where F is the net force, m is the mass, and a is the acceleration. In this case, the net force will be equal to 1000kg multiplied by the acceleration of 0.5m/s^2, which is 500N. Adding this to the weight of the load, the tension in the cable will be 10300N.

c) When the load is raised with a uniform speed of 1.5m/s, the tension in the cable will be equal to the weight of the load, as there is no acceleration. Therefore, the tension will be 9800N.

d) When the load is lowered with an acceleration of 1m/s^2, the tension in the cable will be equal to the weight of the load minus the force required to accelerate it. Using the same equation as in part b, the force required to accelerate the load will be 1000kg multiplied by 1m/s^2, which is 1000