University:
University of Central Arkansas
Course:
MATH 3364 | Concepts of Geometry and Measurement
Academic year:

2021
Views:

294

Pages:

8
Author:

Dayami Obrien

Equilibrium Worksheet #1 Key 1. What is the magnitude and direction of the force necessary to produce equilibrium in the following? ΣFx = 8.0N cos 60° + 5.0N cos 30° ΣFx = 0.33 N ΣFy = 8.0N sin 60° + 5.0N sin 30° ΣFy = 0.428 N tan θ = 0.428 / 0.33 θ = 52.5° F = 0.54 N [52.5°] 2. What is the magnitude and direction of the force needed to produce equilibrium with F1 and F2? ΣFx = 10 cos 60° + 5 cos 45° ΣFx = 12.2 N ΣFy = 10 sin 60° + 5 sin 45° ΣFy = 12.0 N F = 17.0 N [83.8° S of E] 3. An object on which the force of gravity is 50 N is supported by two strings as shown below. Calculate the magnitude of the force of tension exerted by each string. tan 30° = F2 / 50 N cos 30° = 50 / F1 F1 = 58 N F2 = 29 N 4. A boy weighing 400 N hangs on the middle of a rope stretched between two trees. The rope sags in such a way that it makes an angle of 170° at the boy's hands. What is the tension in each rope? T1 = T2 sin85° = 400 / T1 T1 = T2 = 2294.7 N 5. A 660 N object is suspended from a rope which makes an angle of 20° with the wall as shown below. What is the magnitude of the horizontal force necessary to produce equilibrium? tan 20° = F / 660 N F = 240 N 6. A 500 N crate is suspended from a cable in such a manner that the cable makes an angle of 30° with the ceiling at one end and an angle of 60° with the ceiling at the other end. Calculate the tension force exerted by each cable on the crate. sin 60° = T1 / 500 N cos 60° = T2 / 500 N T1 = 433 N T2 = 250 N Answers: 0.54 N, 53° S of W 12.3 N, 83° S of E 29 N, 58 N 2.29 x 10³ N 240 N T1 = 433 N, T2 = 250 N Equilibrium Worksheet #2 Key (Name) A lamp is supported between two vertical poles with two wires attached to the poles as shown. The lamp hangs from a short chain. If the lamp has a mass of 11 kg, what is the tension in the shorter wire? sin 60° = 107.8 / T1 T1 = 93 N As an airplane accelerates along a horizontal runway, a pendulum hanging from its ceiling is displaced 12° from the vertical. Calculate the acceleration of the plane. tan 78° = g / a a = g / tan 78° a = 2.1 m/s² A uniform ladder has a mass of 16 kg and a length of 8.5 m. It stands on the ground and leans against a vertical wall, making an angle of 62° with the ground. The friction between the ladder and the wall is not significant. What is the smallest force of friction between the ladder and the ground which will just prevent the ladder from slipping? H cos 28° * 8.5 m = 16 * 9.8 * 4.25 cos 62° H = 41.7 N Ff = 42 N The following diagram shows a cart on a ramp which is fixed to the floor in the back of a truck. Friction in the wheels of the cart is negligible. At what rate must the truck accelerate forward for the cart to remain stationary with respect to the ramp? Fxa = Fxg μ(acc. 23°) = mg sin 23° a = 4.16 m/s²

Equilibrium worksheets with keys

Related Documents

Recommended Documents

Description

Related Documents

Free up your schedule!

Take 5 seconds to unlock