6. Intro to Forces (Dynamics)

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 6750-kg helicopter accelerates upward at 0.80m/s² while lifting a 1080-kg frame at a construction site, Fig. 4–66. What is the tension in the cable (ignore its mass) which connects the frame to the helicopter?

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?

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?

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?

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?

A book is sitting at rest on a horizontal desk. Which statement best describes the normal force acting on the book?

Why is the support force on an object often called the $\mathrm{normal}$ force?

A roller coaster car of mass $m$ passes over a hill at point $d$ with speed $v$. The radius of curvature of the hill at point $d$ is $r$. What is the normal force exerted on the rider when passing point $d$?

You walk into an elevator, step onto a scale, and push the 'up' button. You recall that your normal weight is $625$ N. Draw a free-body diagram. When the elevator has an upward acceleration of magnitude $2.50$ m/s², what does the scale read?

A woman has a mass of 55 kg. What is her weight while standing on earth?

In the context of vertical forces, in which direction does the normal force $F_n$ act relative to a surface?

At the surface of Jupiter's moon Io, the acceleration due to gravity is $g=1.81$ m/s². A watermelon weighs $44.0$ N at the surface of the earth. What is the watermelon's mass on the earth's surface?