# AP Physics 1 : Tension

## Example Questions

### Example Question #11 : Tension

Earth mass:

Earth's distance from the Sun:

Velocity of the Earth:

Imagine that, instead of gravity, the earth was attached to the sun with a giant, unbreakable rope. Determine what the tension would be in the rope.

Explanation:

The velocity of the earth is

Convert to :

Plug in values:

### Example Question #12 : Tension

An elevator accelerates upward for a short period of time at a rate of . A mass of  is hung by a rope from the top of the elevator.

During the period when the elevator is accelerating, what is the magnitude of the tension in the rope?

Explanation:

Here is a (simplistic) diagram of the elevator. There are three forces acting on this object. There is it's own weight due to gravity ; the tension in the rope holding it up, which we will call ; and there is an external force  due to the fact that the elevator is accelerating upward. Since the mass is fixed, it has zero velocity with respect to the elevator, and therefore the net force on the mass is 0 by Newton's 2nd law. The net force is given by . Solving this equation for  and plugging in the values gives us:

Since we want the magnitude of the tension, and not the value of the vector, we omit the minus sign. Therefore the tension in the rope is , as desired.

### Example Question #13 : Tension

Suppose that a  object is lifted upwards while hanging to a rope. If the object accelerates upwards at a rate of , what is the tension in the rope?

Explanation:

For this question, we're presented with a scenario in which an object of a given mass is hanging to a rope. That rope is being pulled on, causing the object to accelerate upwards at a certain rate. We're then asked to calculate the tension that results in the rope.

In order to answer this question, it's best if we approach this by examining a force diagram. Since there are no pertinent forces occurring in the x direction, the only concern we have is in the y direction.

One of the forces acting on the object is the downward force of gravity. Another force is the upward tension caused by the rope. Hence, we know what force components contribute to the net force. Furthermore, we're told that as it is pulled up, the object accelerates at a rate of . Since this is the net acceleration in the y direction, we can determine the net force in the y direction.

Next, we can rearrange the above terms in order to isolate the term for tension.

Finally, if we plug in the values that we know, we can calculate our answer.

### Example Question #11 : Tension

Two objects of equivalent mass are attached with a very strong rope that goes through a pulley. The masses are left to hang. What will happen?

The masses will remain motionless.

Both masses will fall.

Both masses will rise.

One mass will fall and the other will rise.

None of these

The masses will remain motionless.

Explanation:

The masses will each provide an equal force to each other through the rope. Thus, there will be no net force and no net acceleration.

### Example Question #11 : Tension

Four ropes are used to lift a car with a vertical acceleration of . Determine the tension in an individual rope.

Explanation:

Using superposition of forces and definition of force:

All four ropes will be providing the same force.

Combining equations

Solving for , the force of tension in one rope:

Plugging in values, remembering that gravity is pointing down and thus will be a negative number.

### Example Question #15 : Tension

Suppose that a person is pulling a  box tied to a string across the ground, as shown in the diagram below.

If the string is situated at an angle of  with respect to the horizontal and the coefficient of kinetic friction of the box with respect to the ground is , what tension in the string is necessary so that the box moves at a constant speed?

There is not enough information given to answer this question

Explanation:

To answer this question, we need to separately consider the component forces acting in the horizontal and vertical direction.

First, let's consider the vertical component. Since the box is only moving in the horizontal direction, we know that there are no net forces acting in the vertical direction. Consequently, the net force in the y-direction is zero.

Next, let's look at the forces acting in the horizontal direction. Since we need to figure out the force in the string necessary to make the box move at a constant speed, we're looking for a situation in which the box is not accelerating in the horizontal direction. Thus, we're looking for a case in which the net force in the x-direction is zero.

Now, let's rewrite the expression for the force of kinetic friction.

Now, plugging in the expression for the normal force, we obtain the following.

Next, let's go ahead and plug in the values given to us in the question stem.

### Example Question #11 : Tension

toy is held to a hook on the ceiling with fishing line, determine the tension in the line.

None of these

Explanation:

### Example Question #12 : Tension

toy if being lifted to the ceiling at  by a fishing line. Determine the tension in the line.

Explanation:

### Example Question #13 : Tension

A crane is used to lift a safe of mass  at . Determine the tension in the cable between the crane and the safe.

None of these

Explanation:

### Example Question #201 : Forces

A  string is used to hold up a  rock. The nickel is swaying back and forth. At the bottom of the swing, the rock is moving at . Determine the tension in string at this time.

None of these

Explanation:

The swinging back and forth motion is a part of a circle, thus

Combining equations

There will be the force of gravity and the string acting on the coin

Solving for tension:

Converting and plugging in values: