Tension Transitional Reasoning Practice

Questions

1. 1.

   A maintenance technician with a mass of 70 kg stands on a 10 kg suspended work platform. A light, inextensible rope attached to the platform runs over an ideal overhead pulley fixed to the ceiling, and its free end is held by the technician. To accelerate the technician and platform upward together at a steady rate of $1.5\text{ m/s}^2$, with what magnitude of tension force must the rope be pulled? (Assume the pulley is frictionless and massless, and take $g = 10\text{ m/s}^2$.)

   • A) 920 N
   • B) 800 N
   • C) 400 N
   • D) 460 N
2. 2.

   A heavy-duty hoist lifts a 40 kg cargo container vertically upward using a uniform steel cable of mass 10 kg. The crane winches the assembly so that it accelerates upward at a constant rate of $2.0\text{ m/s}^2$. Taking $g = 10\text{ m/s}^2$ and neglecting air resistance, what is the tension force at the midpoint of the lifting cable?

   • A) 540 N
   • B) 480 N
   • C) 600 N
   • D) 450 N
3. 3.

   During a rail test, an inspection cart accelerates uniformly along a straight horizontal track. Inside the cart, a 0.40 kg sensor sphere hangs from the ceiling by a light cord and remains deflected at a steady angle of 37° to the vertical. Taking $g = 10\text{ m/s}^2$, $\sin 37^\circ = 0.60$, and $\cos 37^\circ = 0.80$, what is the tension in the cord?

   • A) 3.0 N
   • B) 4.0 N
   • C) 5.0 N
   • D) 3.2 N
4. 4.

   A deep-sea research probe of mass 500 kg is lowered vertically into the water by a heavy-duty support cable. As it nears the ocean floor, the crane winch slows the descending probe uniformly from a downward speed of 6.0 m/s to a complete stop over a vertical distance of 9.0 m. Assuming buoyant forces and water resistance are negligible and taking the acceleration due to gravity as 10 m/s², what is the tension in the cable during this slowing phase?

   • A) 1000 N
   • B) 4000 N
   • C) 6000 N
   • D) 5000 N
5. 5.

   An autonomous field rover of mass 60 kg tows a sensor trailer of mass 40 kg along a straight, horizontal gravel track. The rover engine generates a constant forward horizontal thrust of 350 N, while the rover and trailer encounter constant kinetic friction forces of 90 N and 60 N, respectively. If the horizontal coupling connecting them is a light tow hitch, what is the magnitude of the tension force in the hitch during this motion?

   • A) 80 N
   • B) 120 N
   • C) 140 N
   • D) 200 N
6. 6.

   In an experiment demonstrating Newton's second law, two blocks with masses of 3.0 kg and 2.0 kg are connected by a light, inextensible cord draped over a frictionless, massless pulley. When the system is released from rest, the heavier mass accelerates downward while the lighter mass accelerates upward under gravity ($g = 10\text{ m/s}^2$). What is the magnitude of the tension force in the cord during this motion?

   • A) 20 N
   • B) 24 N
   • C) 25 N
   • D) 30 N
7. 7.

   During a warehouse loading operation, a motorized winch pulls a 10 kg crate up a ramp inclined at 37° to the horizontal using a light cable parallel to the surface. The coefficient of kinetic friction between the crate and the ramp is 0.25, and the crate accelerates up the incline at a constant rate of $2.0\text{ m/s}^2$. Taking $g = 10\text{ m/s}^2$, $\sin 37^\circ = 0.60$, and $\cos 37^\circ = 0.80$, what is the tension force exerted by the cable on the crate?

   • A) 60 N
   • B) 80 N
   • C) 115 N
   • D) 100 N
8. 8.

   To safely suspend an 80 kg theatrical lighting fixture, stage technicians secure it using two identical light cables anchored symmetrically to the ceiling. Each cable makes an angle of 30° with the horizontal ceiling, and the entire assembly remains motionless. Taking the acceleration due to gravity as 10 m/s2, what is the tension force exerted by each individual cable?

   • A) 400 N
   • B) 800 N
   • C) 924 N
   • D) 1600 N
9. 9.

   To evaluate the tensile durability of a lightweight tether, engineers connect a 3.0 kg sensor carriage on a smooth, frictionless horizontal rail to a 2.0 kg hanging counterweight using a light cord passing over an ideal pulley. Upon releasing the assembly from rest, the system accelerates freely under gravity with $g = 10\text{ m/s}^2$. What is the magnitude of the tension force maintained in the cord during this motion?

   • A) 12 N
   • B) 20 N
   • C) 8 N
   • D) 15 N
10. 10.

    An autonomous delivery drone ascends vertically with an upward acceleration of $2.0\text{ m/s}^2$, carrying two sensor packages connected in series. Package 1 (mass 3 kg) is suspended directly from the drone by Cable 1, and Package 2 (mass 2 kg) is suspended beneath Package 1 by Cable 2. Neglecting air resistance and cable mass, and taking $g = 10\text{ m/s}^2$, what are the tension forces in Cable 1 and Cable 2, respectively?

    • A) 50 N in Cable 1 and 20 N in Cable 2
    • B) 60 N in Cable 1 and 24 N in Cable 2
    • C) 36 N in Cable 1 and 24 N in Cable 2
    • D) 40 N in Cable 1 and 16 N in Cable 2

Answers and step-by-step solutions appear after you finish the test.