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

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 ?

• A10 N
• B5.0 N
• C30 N
• D7.5 N
• E15 N

What is the magnitude of ?

• A15 N
• B5.0 N
• C30 N
• D10 N
• E7.5 N

What is the magnitude of ?

• A5.0 N
• B30 N
• C15 N
• D10 N
• E7.5 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?

• A18.0 N
• B176 N
• C353 N
• D36.0 N
• E88.2 N

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

• A0
• B36.0 N
• C88.2 N
• D176 N
• E353 N

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

• A0
• B176 N
• C353 N
• D36.0 N
• E88.2 N

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

• A18.0 N
• B176 N
• C353 N
• D36.0 N
• E706 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 ?

Q10:

Two objects are connected to each other by a rope, as shown in the diagram. The angle between a line parallel to the surface the objects are placed on and the direction of the rope that connects the objects is . A second rope is connected to the smaller object. 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 in the direction of at 0.44 m/s2 across a smooth surface. The larger object has a mass of 25 kg and the smaller object has a mass of 7.5 kg. 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 difference between the magnitudes of and .

Find the magnitude of the horizontal component of .

Q11:

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 accelerate in the direction of at 1.2 m/s2 across a smooth surface. The larger object has a mass of 15 kg and the smaller object has a mass of 5.5 kg. 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.

What is the tension in the rope that is applied to?

• A7.0 N
• B11 N
• C18 N
• D25 N
• E21 N

What is the tension in the rope connecting the objects?

• A21 N
• B7.0 N
• C11 N
• D18 N
• E25 N

Q12:

Two objects are connected to each other by a rope, as shown in the diagram. A second rope is connected to the smaller object. A short time after a constant force is applied to the end of the second rope, both objects accelerate horizontally at 0.72 m/s2 across a smooth surface. The larger object has a mass of 18 kg and the smaller object has a mass of 11 kg. A short time after the force is applied, a tension is produced in the rope with force applied to it and a tension is produced in the rope connecting the objects. If , which of the ropes has a direction that makes a greater angle between it and a line parallel to the surface that the objects move along: the rope with force applied to it or the rope connecting the objects?

• ABoth ropes make the same angle as each other.
• BThe rope with the force applied to it makes a greater angle.
• CThe rope that connects the objects makes a greater angle.

Q13:

An object with a mass of 17 kg is at rest, 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. The tensions in the ropes are and 130 N. The direction of the rope with the tension 130 N makes a angle with a line parallel to the surface of the object.

Find the counterclockwise angle that the direction of the rope with tension makes with the line parallel to the surface of the object.

Find the magnitude of .

Q14:

An object with a weight of 85 N is at rest on a smooth slope that is angled above the horizontal, as shown in the diagram. A horizontal rope is attached to the object. At the top of the slope, the rope vertically suspends at rest a second object. The mass of the rope is negligible. What is the ratio of the magnitude of tension to the magnitude of tension ? Answer to two significant figures.

Q15:

Two objects are connected by a pair of ropes, as shown in the diagram. The two ropes meet at the midpoint of the height of the larger object. The other ends of the ropes are attached to the top and bottom of the smaller object. A third rope is connected to the larger object. 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 in the direction of at 2.1 m/s2 across a smooth surface. The larger object has a mass of 7.7 kg and the smaller object has a mass of 3.3 kg. Tension is produced in the rope that the force is applied to and tensions and are produced in the ropes that connect the objects.

What is the ratio of the magnitudes of to ?

What is the ratio of the magnitude of to the magnitude of the horizontal component of ?

What is the angle between the two ropes that connect the objects if has a magnitude of 6.2 N? Answer to the nearest degree.

Q16:

An object with a mass of 18 kg is at rest, suspended vertically from a platform by three 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. The tensions in the ropes are 150 and 135 N. The direction of the rope with the tension of 150 N makes a angle with a line parallel to the surface of the object.

Find the counterclockwise angle that the direction of the rope with tension 135 N makes with the line parallel to the surface of the object.

Find the magnitude of .

Q17:

An object with a weight of 75 N is at rest on a smooth slope that is angled above the horizontal, as shown in the diagram. A horizontal rope is attached to the object and to the top of the slope. The mass of the rope is negligible. What is the magnitude of the tension in the rope?

Q18:

An object with a weight of 150 N is at rest, 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. The tensions in the ropes are and respectively. The directions of these ropes make angles of and , respectively, with a line parallel to the surface of the object. What is the ratio of to ? Answer to three significant figures.

Q19:

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, the objects accelerate horizontally across a smooth surface. The larger object has a mass of 22 kg and the smaller object has a mass of 14 kg. 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. While the objects move, the larger object changes shape and the direction of the rope connecting the objects changes the angle that the rope makes with a line parallel to the surface the objects are moving on. What is the value of when the tensions in the ropes are of the same magnitude?

Q20:

Two objects are both at rest, suspended vertically from a platform by ropes, as shown in the diagram. The smaller object has a weight of 24.5 N and the larger object has a weight of 44.1 N. The weights of the ropes are negligible. The smaller object is suspended by ropes that have tensions of and , where . The larger object is suspended by ropes that have tensions of and , where . The objects are connected by a rope that has a tension of . What is the sum of and ?