# Worksheet: Tension Forces

In this worksheet, we will practice determining the tension forces acting on flexible objects that connect the members of systems of rigid objects.

Q1:

Two identical objects are connected to each other by a rope as shown in the diagram. A second rope is connected to one of the objects. The masses of the ropes are negligible. A short time after constant force is applied to the end of the second rope, both objects uniformly accelerate in the direction of across a smooth surface. Tension is produced in the rope that the force is applied to, and tension is produced in the rope that connects the objects. Which of the following statements correctly represents the relationship between and ?

• A
• B
• C
• D

Q2:

An object with a mass of 25 kg is at rest, suspended vertically from a platform by two ropes, as shown in the diagram. The masses of the ropes are negligible. What is the angle between the two ropes at the point that they connect to the object?

Q3:

Two objects of mass 13 kg each are connected to each other by a rope, as shown in the diagram. A second rope is connected to one of the objects. The angle between a line parallel to the surface the objects are placed on and the direction of the second rope is . The masses of the ropes are negligible. A short time after a constant force is applied to the end of the second rope, both objects accelerate horizontally across a smooth surface. A short time after the force is applied, a tension is produced in the rope that the force is applied to and a tension is produced in the rope that connects the objects.

Find the acceleration of the objects.

Find .

Q4:

Two objects are connected to each other by a rope, as shown in the diagram. A second rope is connected to the smaller object. The mass of the ropes is negligible. A short time after a constant force is applied to the end of the second rope, both objects uniformly accelerate in the direction of across a smooth surface. Tension is produced in the rope that the force is applied to, and tension is produced in the rope that connects the objects.

Which of the following free-body diagrams correctly represents the directions and magnitudes of the forces acting horizontally on the smaller block?

• A
• B
• C
• D

Which of the following free-body diagrams correctly represents the direction and magnitude of the force acting horizontally on the larger block?

• A
• B
• C
• D

Q5:

An object with a mass of 22 kg is suspended vertically from a platform by two ropes, as shown in the diagram. The masses of the ropes are negligible. The topmost face of the object is parallel to the platform from which it is suspended.

Find the magnitude of the net acceleration of the object.

Is the object’s horizontal acceleration toward the left or the right?

• AThe horizontal acceleration is zero.
• BThe horizontal acceleration is toward the right.
• CThe horizontal acceleration is toward the left.

What is the clockwise angle that the direction of the object’s net acceleration makes below a line parallel to the topmost surface of the object? Answer to the nearest degree.

Q6:

Two identical objects are connected by a rope, and an additional rope is connected to the side of each object as shown in the diagram. The masses of the ropes are negligible. The forces and are simultaneously exerted on the ropes that have free ends, where and have magnitudes of 15 N. A short time after the forces are applied, tensions , , and exist in the three ropes.

What is the magnitude of ?

• A 5.0 N
• B 15 N
• C 7.5 N
• D 30 N
• E 10 N

What is the magnitude of ?

• A 5.0 N
• B 30 N
• C 15 N
• D 7.5 N
• E 10 N

What is the magnitude of ?

• A 7.5 N
• B 10 N
• C 30 N
• D 15 N
• E 5.0 N

Q7:

Two objects, each with a mass of 18.0 kg, are at rest and suspended vertically from a platform by ropes that have tensions and , as shown in the diagram. The masses of the ropes are negligible.

What is the magnitude of the vertically downward force that acts on the lower object due to its weight?

• A 18.0 N
• B 353 N
• C 88.2 N
• D 36.0 N
• E 176 N

What magnitude of vertically upward force does the rope connecting the objects exert on the lower object?

• A 176 N
• B 36.0 N
• C 88.2 N
• D0
• E 353 N

What magnitude of vertically downward force does the rope connecting the objects exert on the upper object?

• A 353 N
• B 176 N
• C0
• D 88.2 N
• E 36.0 N

What magnitude of vertically downward force acts on the rope suspending the upper object?

• A 353 N
• B 36.0 N
• C 176 N
• D 706 N
• E 18.0 N

Q8:

Three identical objects are all at rest, suspended vertically from a platform by ropes, as shown in the diagram. Each identical object has a mass of 1.4 kg. A rope is connected from each of the identical objects to an object that has a mass of 1.8 kg, vertically suspended at rest below. The masses of the ropes are negligible. The tension in each of the ropes connected to the 1.8 kg mass object is the same.

Find the magnitude of .

Find the magnitude of .

Q9:

An object with a mass of 2.4 kg is placed between two other objects with a mass of 6.2 kg each. The objects are all connected to each other by ropes, as shown in the diagram. The masses of the ropes are negligible. A short time after a constant force is applied to the end of the first rope, the three objects accelerate in the direction of at 1.5 m/s2 across a smooth surface. The tensions produced in the three ropes are , , and .

What is the ratio of to ?

What is the ratio of to ?