Two ropes are attatched to a tree, and forces (in Newtons) of \(\vec{F}^{T}_{tree,r_1} = 2.0\hat{x} + 4.0\hat{y}\) and \(\vec{F}^{T}_{tree,r_2} = 3.0\hat{x} + 6.0\hat{y}\) are applied. The forces are coplanar (in the same plane).
(a) What is the resultant (net force) of these two force vectors?
(b) Find the magniude and direction of this net force.
Calculation3.8.2.Telephone Pole Secured by Cables.
A telephone pole has three cables pulling as shown in the figure, with \(\vec{F}^{T}_{pole,c_1} = (300.0\hat{x} + 500.0\hat{y})\text{,}\)\(\vec{F}^{T}_{pole,c_2} = -200.0\hat{x}\text{,}\) and \(\vec{F}^{T}_{pole,c_3} = -800.0\hat{y}\text{.}\)
(a) Find the net force on the telephone pole in component form.
(b) FInd the magnitude and direction of this net force.
Calculation3.8.3.Forces at an Angle on a Tree.
Two teenagers are pulling on ropes attached to a tree. The angle between the ropes is 30.0\(°\text{.}\) David pulls with a force of 400.0 N and Stephanie pulls with a force of 300.0 N.
(a) Find the component form of the net force.
(b) Find the magnitude of the resultant (net) force on the tree and the angle it makes with David’s rope.
Calculation3.8.4.Balancing Three Forces.
Two forces of \(\vec{F}_1 = \frac{75.0}{\sqrt{2}}(\hat{x} - \hat{y})\) N and \(\vec{F}_2 = \frac{150.0}{\sqrt{2}}(\hat{x} - \hat{y})\) N act on an object.
Find the third force \(\vec{F}_3\) that is needed to balance the first two forces.
Calculation3.8.5.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 130.0 N and Jennifer’s force is 32\(°\) east of north with a magnitude of 180.0 N.
(a) Find the net force in component form.
(b) Find the magnitude and direction of the net force.
(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?
Calculation3.8.6.A Sprinter’s Force.
Andrea, a 63.0-kg sprinter, starts a race with an acceleration of 4.200 m/s\(^2\text{.}\)
What is the net external force on her?
SubsectionPractice
Calculation3.8.7.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.
