To solve these tension word problems, you will mostly need Newton's second law of motion.
Problem # 1
a 100 kg bucket is being lifted by a rope. The bucket started at rest and after being lifted 4 m, it is moving at 4 m/s. If the acceleration is constant, what is the tension on the rope?
Solution
The diagram below describes the problem and it is useful in order to visualize the problem.
Observations:
F_{T} is the force of tension and it is represented with a bigger vector. This force has to be bigger since it is making the bucket go up.The only missing quantity is a. To get a, we can use one of the constant acceleration equations.
Problem # 2:
A rope is attached to a vehicle weighing 500 kN. A very strong man puts the other end of the rope inside his mouth at an angle of 30 degrees from the horizontal. If the strong man is able to move the vehicle with a constant force 1 m away with a speed of 0.25 m/s, what is the tension on the rope. (Use g = 10 m/s^{2})
Solution
This situation is shown below with graph.
Newton's second law gives F = ma
Since the vehicle is only moving along the x axis, the only force on the vehicle is along the x axis.
We get F_{x} = ma_{x}Since the man is moving the vehicle with a constant force, the
acceleration is constant. Therefore, we can use the following equation
again to get the acceleration.
Notice how important it was to use one of the constant acceleration equations to solve the two tension word problems above. Many problems in physics have a constant acceleration. Therefore, try to become familiar to these equations since they will keep coming back when solving word problems.
Jan 26, 23 11:44 AM
Jan 25, 23 05:54 AM