6. Intro to Forces (Dynamics)

A fisherman yanks a fish vertically out of the water with an acceleration of 2.5 m/s² using very light fishing line that has a breaking strength of 18 N (≈ 4lb). The fisherman unfortunately loses the fish as the line snaps. What can you say about the mass of the fish?

A light rope is attached to a block with mass $4.00$ kg that rests on a frictionless, horizontal surface. The horizontal rope passes over a frictionless, massless pulley, and a block with mass $m$ is suspended from the other end. When the blocks are released, the tension in the rope is $15.0$ N. How does the tension compare to the weight of the hanging block?

Three sleds are being pulled horizontally on frictionless horizontal ice using horizontal ropes (Fig. E$5.14$). The pull is of magnitude $190$ N. Find the tension in ropes $A$ and $B$.

Two $25.0$-N weights are suspended at opposite ends of a rope that passes over a light, frictionless pulley. The pulley is attached to a chain from the ceiling. What is the tension in the chain?

Two $25.0$-N weights are suspended at opposite ends of a rope that passes over a light, frictionless pulley. The pulley is attached to a chain from the ceiling. What is the tension in the rope?

A $550$-N physics student stands on a bathroom scale in an elevator that is supported by a cable. The combined mass of student plus elevator is $850$ kg. As the elevator starts moving, the scale reads $450$ N. Find the acceleration of the elevator (magnitude and direction).

A light rope is attached to a block with mass $4.00$ kg that rests on a frictionless, horizontal surface. The horizontal rope passes over a frictionless, massless pulley, and a block with mass $m$ is suspended from the other end. When the blocks are released, the tension in the rope is $15.0$ N. What is the acceleration of either block?

Three sleds are being pulled horizontally on frictionless horizontal ice using horizontal ropes (Fig. E$5.14$). The pull is of magnitude $190$ N. Find the acceleration of the system.

A light rope is attached to a block with mass $4.00$ kg that rests on a frictionless, horizontal surface. The horizontal rope passes over a frictionless, massless pulley, and a block with mass m is suspended from the other end. When the blocks are released, the tension in the rope is $15.0$ N. Find $m$.

A $750.0$-kg boulder is raised from a quarry $125$ m deep by a long uniform chain having a mass of $575$ kg. This chain is of uniform strength, but at any point it can support a maximum tension no greater than $2.50$ times its weight without breaking. How long does it take to be lifted out at maximum acceleration if it started from rest?

A $75.0$-kg wrecking ball hangs from a uniform, heavy-duty chain of mass $26.0$ kg. What is the tension at a point three-fourths of the way up from the bottom of the chain?

A 50 kg box hangs from a rope. What is the tension in the rope if: The box has v_y = 5.0 m/s and is speeding up at 5.0 m/s²

A 50 kg box hangs from a rope. What is the tension in the rope if: The box moves up at a steady 5.0 m/s?

Astronauts in space 'weigh' themselves by oscillating on a spring. Suppose the position of an oscillating 75 kg astronaut is given by $x=\left(0.30\text{m}\right)\sin \left(\right(\pi \text{rad/s})\times t)$, where t is in s. What force does the spring exert on the astronaut at (a) t = 1.0 s and (b) 1.5 s? Note that the angle of the sine function is in radians.

The mass of the sun is 2.0 x 10³⁰ kg. A 5.0 x 10¹⁴ kg comet is 75 million kilometers from the sun. What is the magnitude of the comet's acceleration toward the sun?