Two ropes are attatched to a tree, and forces of \(\vec{F}^{T}_{tree,r_1} = 2\hat{x} + 4\hat{y} \mathrm{~N}\) and \(\vec{F}^{T}_{tree,r_2} = 3\hat{x} + 6\hat{y} \mathrm{~N}\) are applied.
The magnitude is \(F_{net} = 11 ~\mathrm{N}\text{,}\) and the direction is \(\theta = 63°\)
Calculation3.9.2.Telephone Pole Secured by Cables.
A telephone pole has three cables pulling with \(\vec{F}^{T}_{pole,c_1} = (300\hat{x} + 500\hat{y}) \mathrm{~N}\text{,}\)\(\vec{F}^{T}_{pole,c_2} = -200\hat{x} \mathrm{~N}\text{,}\) and \(\vec{F}^{T}_{pole,c_3} = -800\hat{y} \mathrm{~N}\text{.}\)
(a)
Find the net force on the telephone pole in component form.
(b)
Find the magnitude and direction of this net force.
Calculation3.9.3.Balancing Three Forces.
Two forces of \(\vec{F}_1 = \frac{75.0}{\sqrt{2}}(\hat{x} - \hat{y}) ~\mathrm{N}\) and \(\vec{F}_2 = \frac{150.0}{\sqrt{2}}(\hat{x} - \hat{y}) ~\mathrm{N}\) act on an object.
Find the third force \(\vec{F}_3\) that is needed to balance the first two forces.
Calculation3.9.4.Pushing the Couch.
While sliding a couch across a floor, Andrea and Jennifer exert forces \(\vec{F}_A\) and \(\vec{F}_J\) on the couch. Andrea’s force is due north with a magnitude of \(130 ~\mathrm{N}\) and Jennifer’s force is \(32°\) east of north with a magnitude of \(180 ~\mathrm{N}\text{.}\)
\(F_{net} = 299 ~\mathrm{N}\) at \(71°\) north of east
(c)
If Andrea and Jennifer’s housemates, David and Stephanie, disagree with the move and want to prevent its relocation, with what combined force \(\vec{F}_{DS}\) should they push so that the couch does not move?
Vivenna, a \(63 ~\mathrm{kg}\) sprinter, starts a race with an acceleration of \(4.2 ~\mathrm{m/s^2}\text{.}\)
What is the net external force on Vivenna?
Calculation3.9.6.Cleaner Pushing a Cart.
A cleaner pushes a \(4.5 \mathrm{~kg}\) laundry cart in such a way that the net external force on it is \(60 \mathrm{~N}\text{.}\) Calculate the magnitude of his cart’s acceleration.
Calculation3.9.7.Accelerating Rocket I.
A rocket sled (with its rockets off) accelerates opposite its direction of motion at a rate of \(196 ~\mathrm{m/s^2}\text{.}\) The mass of the rocket is \(2.1 \times 10^3 ~\mathrm{kg}\text{.}\)
What force is necessary to produce this acceleration opposite to the motion?
Suppose the rocket sled from the previous activity starts with one rocket burning. Assume that the mass of the system is \(2.10 \times 103 ~\mathrm{kg}\text{,}\) the thrust is \(2.40 \times 10^4 ~\mathrm{N}\text{,}\) and the force of friction opposing the motion is \(650 ~\mathrm{N}\text{.}\)
What is the magnitude of this acceleration?
Calculation3.9.9.Sliding Frictionless Block.
A \(M = 10 \mathrm{~kg}\) block slides on a frictionless surface. Suppose two forces are acting on the block, each with magnitude \(F = 30 ~\mathrm{N}\text{.}\) One force acts horizontally to the right, while the other acts down and to the right such that it makes a \(30^o\) angle with the horizontal.
What is the magnitude of the resulting acceleration of the block?
SubsectionAdditional Practice
Calculation3.9.10.Balancing the forces.
Each of the following (2-dimensional) free-body diagrams shows the directions of all the forces that are acting on an object. If the magnitude of each force can be adjusted to any non-zero value but its direction cannot be changed, which of the objects can be put into equilibrium?
A person pushes a cart to the left at constant velocity across a level floor. A teapot sits on the cart without slipping. Assume there is no air resistance. Choose the correct free-body diagram for the teapot.
You are trying to exercise your cat by walking them around the room with a harness - a jacket is strapped around the cat with a leash that you can pull. To get your cat moving, you pull on the leash at an angle \(\theta\) above the horizontal (note this is not how you should train your cat with a harness). Annoyed, your cat flops onto their side where there is a sizable friction between the cat and the floor. As you pull your cat, you notice they move with a constant speed.
From previous experiments with this harness, you know that your "pull" at the given angle has a vertical component equal to half the weight of your cat.
(a)Rank the forces.
During the pull, rank the magnitude of the forces acting on the cat.
To assist you, you add an additional rope hanging from the ceiling that always stays vertical but the attachment is free to move along the ceiling (like something you would find in an action movie). This new rope’s tension has a magnitude equal to the vertical component of your pull. You now pull on the leash with the same magnitude and direction as before.
(b)Explain.
Now, you notice the cat speeds up. Explain why this occurs.
ReferencesReferences
[1]
Practice activities adapted from OpenStax: https://openstax.org/books/university-physics-volume-1/pages/5-problems.
[2]
Additional practice activities from BoxSand: https://boxsand.physics.oregonstate.edu/.
