In this worksheet, we will practice calculating resultant forces in systems involving strings, ropes, and wires under tension.

**Q1: **

Consider the baby being weighed in the shown figure.

What is the mass of the infant and basket if a scale reading of 55 N is observed?

What is tension in the cord attaching the baby to the scale?

What is tension in the cord attaching the scale to the ceiling, if the scale has a mass of 0.500 kg?

**Q3: **

Two teams of nine members each engage in tug-of-war. The members of one team have an average mass of 68 kg and exert an average horizontal force of N. The members of the other team have an average mass of 73 kg and exert an average horizontal force of N.

What is magnitude of the acceleration of the two teams?

What is the tension in the section of rope between the teams?

- A
- B N
- C N
- D N
- E N

**Q4: **

A lift filled with passengers has a mass of kg. Initially, the lift accelerates vertically upward at 1.20 m/s^{2} for 1.50 s. After accelerating, the lift moves with constant velocity for 8.50 s, and then decelerates at 0.600 m/s^{2} for 3.00 s.

What is the magnitude of the tension in the cable holding the lift during the lift’s initial acceleration?

- A N
- B N
- C N
- D N
- E N

What is the magnitude of the tension in the cable holding the lift while the lift is moving at constant velocity?

- A N
- B N
- C N
- D N
- E N

What is the magnitude of the tension in the cable holding the lift during the lift’s deceleration?

- A N
- B N
- C N
- D N
- E N

What is the vertical upward displacement of the lift from the point where its acceleration began to the point where its deceleration finished?

- A 19.4 m
- B 20.4 m
- C 19.8 m
- D 18.7 m
- E 19.1 m

What is the lift’s final velocity?

- A m/s
- B 0.957 m/s
- C 1.06 m/s
- D 0.00 m/s
- E m/s

**Q5: **

As shown in the figure, if what is the tension in string 1?

**Q6: **

A ball of mass 11.5 g hangs from the roof of a freight car by a string. While the freight car accelerates, the string makes an angle of with the vertical.

What is the magnitude of the acceleration of the freight car?

What is the magnitude of the tension in the string?

**Q7: **

Two blocks are connected across a pulley by a rope as shown. The mass of the block on the table is 4.0 kg and the mass of the hanging block is 1.0 kg. The mass of the rope is negligible. The table and the pulley are both frictionless.

Find the acceleration of the system.

Find the tension in the rope.

Find the speed of the hanging block when it hits the floor. Assume that the hanging block is initially at rest and located 1.0 m vertically above the floor.

**Q8: **

A 2.00 kg block (mass 1) and a 4.00 kg block (mass 2) are connected by a light string as shown; the inclination of the ramp is . Friction is negligible.

What is the magnitude of the acceleration of each block (these magnitudes are equal to each other).

What is the magnitude of the tension in the string?

**Q9: **

One end of a 24.5-m-long rope is tied to a tree, while the other end is tied to a car stuck in mud. The motorist pulls on the midpoint of the rope, displacing the rope by 2.0 m perpendicularly to its length. If he exerts a force of 92 N, determine the force exerted on the car.

**Q10: **

An object with mass is connected to another object of the same mass, as shown. What is the tension in the string connecting the objects? Assume the pulley and surface of the slope are frictionless.

**Q11: **

A 0.0502-kg pair of fuzzy dice is attached to the rearview mirror of a car by a short string. The car accelerates at constant rate, and the dice hang at an angle of from the vertical because of the car’s acceleration. What is the magnitude of the acceleration of the car?

**Q12: **

A 30.0-kg-mass girl on a swing is held at rest by a horizontally acting force . The swing’s two ropes are at an angle of with respect to the vertical.

Calculate the magnitude of the tension in both of the ropes supporting the swing.

Calculate the magnitude of

**Q13: **

A 62.2-kg gymnast climbs a rope.

The gymnast climbs the rope at a constant speed. What tension is produced in the rope?

- A N
- B 0 N
- C N
- D N
- E N

The gymnast accelerates while climbing at a rate of
0.36 m/s^{2}.
What tension is produced in the rope?

**Q14: **

A wire is suspended from a ceiling at the point and the point . The wire bears the two loads and at the points and respectively. The anticlockwise angle made by the wire from the vertical at point is and the clockwise angle made by the wire from the vertical at point is . Calculate the tension in the wire segment .

- A 225 kN
- B 190 kN
- C 390 kN
- D 238 kN
- E 475 kN

**Q15: **

A wire is suspended from a ceiling at the point and the point . The wire bears the two loads and at the points and respectively. The counterclockwise angle made by the wire from the vertical at point is and the clockwise angle made by the wire from the vertical at point is . Calculate the tension in the wire segment .

**Q16: **

A wire is suspended from a ceiling at the point and the point . The wire bears the two loads and at the points and respectively. The anticlockwise angle made by the wire from the vertical at point is and the clockwise angle made by the wire from the vertical at point is . Calculate the tension in the wire segment .

- A 225 kN
- B 190 kN
- C 427 kN
- D 390 kN
- E 475 kN

**Q17: **

The coefficient of static friction between a belt and a circular pulley is 0.57. The contact length between the belt and the pulley subtends an angle of 120 degrees. What is the ratio of belt tensions on the tight side (the side that pulls) to the loose side of the pulley that can be accommodated without the belt slipping?

**Q18: **

A rod is used to carry a tensile load of 44.48 kN. The ultimate tensile stress of the material used in the rod is 1.0 GPa. What should be the minimum diameter of the rod to safely carry the load?

**Q19: **

A rope with a length of 5.00 m runs from point to point , as shown in the accompanying diagram. The horizontal distance between the walls is 3.00 m, and so the rope sags. Point is 1.00 m vertically above Point . Between the points and along the rope, a frictionless pulley suspends a load that has a weight of 0.200 kN. Calculate the tension in the rope when the system is at equilibrium.

**Q20: **

Suppose your car was mired deeply in the mud and you wanted to use the method illustrated in the figure to pull it out.

What force would you have to exert perpendicular to the center of the rope to produce a force of 14 000 N on the car if the angle is ?

Real ropes stretch under such forces. What force would be exerted on the car if the angle increases to while you are still applying the force found in the first question to its center?

**Q21: **

The figure shows two superheroes, Gnatman and Sparrow, hanging motionless from a rope. Gnatman is above Sparrow on the rope. Gnatman’s mass is 95.0 kg, Sparrow’s mass is 65.0 kg, and the mass of the rope is negligible.

Find the tension in the rope above Gnatman.

Find the tension in the rope between Gnatman and Sparrow.

**Q22: **

A tightrope walker with a mass of 70 kg stands at the center of a high wire, as shown in the diagram. The wire is supported at its ends and is directed at an angle of below the horizontal. What is the magnitude of the tension in the wire?

**Q23: **

A pan of mass 42.0 g is suspended below a horizontal platform by two strings of lengths 5.00 cm and 10.00 cm, respectively, as shown in the diagram. The pan is loaded until its weight is great enough to cause one of the strings to have a tension greater than 2.80 N, which breaks the string. What is the total mass of the pan and its load that just breaks the string?

**Q24: **

A traffic light of mass 15.0 kg is suspended from two wires that make angles of and above the horizontal respectively, as shown in the diagram.

Find the tension in the angle wire.

Find the tension in the angle wire.

**Q25: **

What force is exerted on the tooth in the figure if the tension in the wire is 25.0 N? Note that the force applied to the tooth is smaller than the tension in the wire, but this is necessitated by the practical considerations of how force can be applied in the mouth.