5.6 Common forces  (Page 8/11)

A table is placed on a rug. Then a book is placed on the table. What does the floor exert a normal force on?

A particle is moving to the right. (a) Can the force on it to be acting to the left? If yes, what would happen? (b) Can that force be acting downward? If yes, why?

A leg is suspended in a traction system, as shown below. (a) Which part of the figure is used to calculate the force exerted on the foot? (b) What is the tension in the rope? Here $\overrightarrow{T}$ is the tension, ${\overrightarrow{w}}_{\text{leg}}$ is the weight of the leg, and $\overrightarrow{w}$ is the weight of the load that provides the tension.

Suppose the shinbone in the preceding image was a femur in a traction setup for a broken bone, with pulleys and rope available. How might we be able to increase the force along the femur using the same weight?

Two teams of nine members each engage in tug-of-war. Each of the first team’s members has an average mass of 68 kg and exerts an average force of 1350 N horizontally. Each of the second team’s members has an average mass of 73 kg and exerts an average force of 1365 N horizontally. (a) What is magnitude of the acceleration of the two teams, and which team wins? (b) What is the tension in the section of rope between the teams?

What force does a trampoline have to apply to Jennifer, a 45.0-kg gymnast, to accelerate her straight up at $7.50{\text{m/s}}^2$ ? The answer is independent of the velocity of the gymnast—she can be moving up or down or can be instantly stationary.

(a) Calculate the tension in a vertical strand of spider web if a spider of mass $2.00\times {10}^{\mathrm{-5}}\text{kg}$ hangs motionless on it. (b) Calculate the tension in a horizontal strand of spider web if the same spider sits motionless in the middle of it much like the tightrope walker in [link] . The strand sags at an angle of $12\text{°}$ below the horizontal. Compare this with the tension in the vertical strand (find their ratio).

Suppose Kevin, a 60.0-kg gymnast, climbs a rope. (a) What is the tension in the rope if he climbs at a constant speed? (b) What is the tension in the rope if he accelerates upward at a rate of $1.50{\text{m/s}}^2$ ?

Show that, as explained in the text, a force $F_{\perp }$ exerted on a flexible medium at its center and perpendicular to its length (such as on the tightrope wire in [link] ) gives rise to a tension of magnitude $T=F_{\perp }\text{/}2\text{sin}\left(\theta \right)$ .

Consider [link] . The driver attempts to get the car out of the mud by exerting a perpendicular force of 610.0 N, and the distance she pushes in the middle of the rope is 1.00 m while she stands 6.00 m away from the car on the left and 6.00 m away from the tree on the right. What is the tension T in the rope, and how do you find the answer?

A bird has a mass of 26 g and perches in the middle of a stretched telephone line. (a) Show that the tension in the line can be calculated using the equation $T=\frac{mg}{2\text{sin}\theta }$ . Determine the tension when (b) $\theta =5\text{°}$ and (c) $\theta =0.5\text{°}$ . Assume that each half of the line is straight.

One end of a 30-m rope is tied to a tree; the other end is tied to a car stuck in the mud. The motorist pulls sideways on the midpoint of the rope, displacing it a distance of 2 m. If he exerts a force of 80 N under these conditions, determine the force exerted on the car.

Consider the baby being weighed in the following figure. (a) What is the mass of the infant and basket if a scale reading of 55 N is observed? (b) What is tension $T_1$ in the cord attaching the baby to the scale? (c) What is tension $T_2$ in the cord attaching the scale to the ceiling, if the scale has a mass of 0.500 kg? (d) Sketch the situation, indicating the system of interest used to solve each part. The masses of the cords are negligible.

What force must be applied to a 100.0-kg crate on a frictionless plane inclined at $30\text{°}$ to cause an acceleration of ${2.0\text{m/s}}^2$ up the plane?

A 2.0-kg block is on a perfectly smooth ramp that makes an angle of $30\text{°}$ with the horizontal. (a) What is the block’s acceleration down the ramp and the force of the ramp on the block? (b) What force applied upward along and parallel to the ramp would allow the block to move with constant velocity?