6.1 Solving problems with newton’s laws  (Page 11/12)

To simulate the apparent weightlessness of space orbit, astronauts are trained in the hold of a cargo aircraft that is accelerating downward at g . Why do they appear to be weightless, as measured by standing on a bathroom scale, in this accelerated frame of reference? Is there any difference between their apparent weightlessness in orbit and in the aircraft?

A 30.0-kg girl in a swing is pushed to one side and held at rest by a horizontal force $\overrightarrow{F}$ so that the swing ropes are $30.0\text{°}$ with respect to the vertical. (a) Calculate the tension in each of the two ropes supporting the swing under these conditions. (b) Calculate the magnitude of $\overrightarrow{F}.$

Find the tension in each of the three cables supporting the traffic light if it weighs 2.00 × 10 ² N.

Three forces act on an object, considered to be a particle, which moves with constant velocity $v=(3\widehat{i}-2\widehat{j})\text{m/s}\text{.}$ Two of the forces are ${\overrightarrow{F}}_1=(3\widehat{i}+5\widehat{j}-6\widehat{k})\text{N}$ and ${\overrightarrow{F}}_2=(4\widehat{i}-7\widehat{j}+2\widehat{k})\text{N}\text{.}$ Find the third force.

A flea jumps by exerting a force of $1.20\times {10}^{\mathrm{-5}}\text{N}$ straight down on the ground. A breeze blowing on the flea parallel to the ground exerts a force of $0.500\times {10}^{\mathrm{-6}}\text{N}$ on the flea while the flea is still in contact with the ground. Find the direction and magnitude of the acceleration of the flea if its mass is $6.00\times {10}^{\mathrm{-7}}\text{kg}$ . Do not neglect the gravitational force.

Two muscles in the back of the leg pull upward on the Achilles tendon, as shown below. (These muscles are called the medial and lateral heads of the gastrocnemius muscle.) Find the magnitude and direction of the total force on the Achilles tendon. What type of movement could be caused by this force?

After a mishap, a 76.0-kg circus performer clings to a trapeze, which is being pulled to the side by another circus artist, as shown here. Calculate the tension in the two ropes if the person is momentarily motionless. Include a free-body diagram in your solution.

A 35.0-kg dolphin decelerates from 12.0 to 7.50 m/s in 2.30 s to join another dolphin in play. What average force was exerted to slow the first dolphin if it was moving horizontally? (The gravitational force is balanced by the buoyant force of the water.)

When starting a foot race, a 70.0-kg sprinter exerts an average force of 650 N backward on the ground for 0.800 s. (a) What is his final speed? (b) How far does he travel?

A large rocket has a mass of $2.00\times {10}^6\text{kg}$ at takeoff, and its engines produce a thrust of $3.50\times {10}^7\text{N}.$ (a) Find its initial acceleration if it takes off vertically. (b) How long does it take to reach a velocity of 120 km/h straight up, assuming constant mass and thrust?

A basketball player jumps straight up for a ball. To do this, he lowers his body 0.300 m and then accelerates through this distance by forcefully straightening his legs. This player leaves the floor with a vertical velocity sufficient to carry him 0.900 m above the floor. (a) Calculate his velocity when he leaves the floor. (b) Calculate his acceleration while he is straightening his legs. He goes from zero to the velocity found in (a) in a distance of 0.300 m. (c) Calculate the force he exerts on the floor to do this, given that his mass is 110.0 kg.