A 10-Lb Object Is Suspended By A String From An Overhead Support.?, A Horizontal Force Of 5.8 Pounds Is Applied On The Object. The Measure Of The Angl
A 10-lb object is suspended by a string from an overhead support.?
A horizontal force of 5.8 pounds is applied on the object. The measure of the angle which the string makes with the horizontal is???
Answer:
φ=60°
Step by step explanation:
Before the horizontal force F is applied:
The gravitational force keeps the string stretched. The string reacts to the gravitational force W by pulling the object upwards with the same amount of force :
After the horizontal force is applied:
The string tilts to one side while the tension T of the string changes direction and finally stops moving when it reaches a static equilibrium with F.
This statement can be written in algebraic form:
Vertically:
∑ ⇔
⇔Tsin(φ) =mgC ⇔ T=mgC/sin(φ)
where C=1/32.17, for the imperial system of units to be coherent.
Horizontally:
∑ ⇔
⇔ F=Tcos(φ)
This is a system of equations, we will solve it by eliminating T.
Substitute T from the previous equation:
F=mgC cos(φ)/sin(φ) ⇔ sin(φ)/cos(φ)=mgC/F ⇔
tan(φ)=
⇔ φ≅60°
In the attached picture you can see the tension T being split into its components on the horizontal and the vertical axis.
Keywords: Force components, Static equilibrium, System of equations
Related Links:
Comments
Post a Comment