# Worksheet: Tension

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

**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 1,350 N. The members of the other team have an average mass of 73 kg and exert an average horizontal force of 1,365 N.

What is magnitude of the acceleration of the two teams?

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

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

**Q4: **

An elevator filled with passengers has a mass of
kg.
Initially,
the elevator accelerates vertically upward at 1.20 m/s^{2} for
1.50 s. After accelerating,
the elevator 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 elevator during the elevatorβs initial acceleration?

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

What is the magnitude of the tension in the cable holding the elevator while the elevator 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 elevator during the elevatorβs deceleration?

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

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

What is the elevatorβs final velocity?

**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?

**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 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 .

**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 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 .

**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?

**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. Gnatmanβs mass is 95.0 kg, Sparrowβs 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.

**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?