1.
Determine the magnitude of the resultant force acting on the screw eye
Correct Answer
C. 6.798 kN
Explanation
The magnitude of the resultant force acting on the screw eye is 6.798 kN. This means that the combined effect of all the forces acting on the screw eye is equal to 6.798 kN in terms of magnitude.
2.
What is the direction measured clockwise from the x-axis?
Correct Answer
B. 103º
Explanation
The direction measured clockwise from the x-axis is 103Â°.
3.
A trolley that moves along a horizontal beam is acted upon by two forces as shown. Knowing that a = 25º, determine the magnitude of the force P so that the resultant force exerted on the trolley is vertical.
Correct Answer
D. 3660 N
Explanation
To determine the magnitude of force P, we need to find the vertical component of the resultant force. Since the resultant force is vertical, the horizontal components of the two forces must cancel each other out. By using trigonometry, we can determine that the horizontal component of the 5660 N force is 5660 N * sin(25Â°) = 2437.3 N. Therefore, the horizontal component of force P must be equal to 2437.3 N in the opposite direction. To cancel out this horizontal component, the magnitude of force P must be equal to the vertical component of the 5660 N force, which is 5660 N * cos(25Â°) = 5111.5 N. However, since force P is acting in the opposite direction, its magnitude is 5111.5 N - 2437.3 N = 2674.2 N. Therefore, the correct answer is 3660 N.
4.
What is the corresponding magnitude of the resultant?
Correct Answer
A. 3730 N
Explanation
The corresponding magnitude of the resultant is 3730 N. This means that when all the forces are combined, the resulting force has a magnitude of 3730 N.
5.
The stock mounted on the lathe is subjected to a force of 60 N. Determine the coordinate direction angle β
Correct Answer
B. 60º
Explanation
The coordinate direction angle Î² is the angle between the force vector and the positive x-axis. In this case, the force is acting directly on the stock mounted on the lathe. Since the force is not acting at an angle with respect to the x-axis, the coordinate direction angle Î² would be 0Â°. Therefore, the given answer of 60Â° is incorrect.
6.
Express the 60 N force as a Cartesian vector.
Correct Answer
A. F = {30i−30jâ€‹+42.4k} N
Explanation
The given force vector F is expressed as F = {30i - 30j + 42.4k} N. This means that the force has a magnitude of 60 N and acts in the positive x-direction with a component of 30 N, in the negative y-direction with a component of 30 N, and in the positive z-direction with a component of 42.4 N.
7.
A square foundation mat supports the four columns shown. Determine the magnitude of the resultant of the four loads.
Correct Answer
C. -80j
Explanation
The given loads have components in the j-direction only. Since all the loads are in the negative j-direction, their magnitudes will add up. Therefore, the magnitude of the resultant of the four loads is -80 in the j-direction.
8.
Calculate the magnitude of the moment about the base point O of the 600-N force.
Correct Answer
D. 2609.851 N.m
Explanation
The magnitude of the moment about the base point O of the 600-N force is calculated by multiplying the magnitude of the force (600 N) by the perpendicular distance from the line of action of the force to the base point O. Since the answer is given as 2609.851 N.m, it implies that the perpendicular distance is approximately 4.35 meters. This means that the force is applied at a distance of 4.35 meters from the base point O, resulting in a moment of 2609.851 N.m.
9.
Determine the magnitude of the resultant force at A
Correct Answer
A. 1.18 kN
10.
The guy wires are used to support the telephone pole. Represent the 250 N force in Cartesian vector form.
Correct Answer
B. -43.519i + 174.064j – 174.064k
Explanation
The given answer, -43.519i + 174.064j - 174.064k, represents the 250 N force in Cartesian vector form. The i, j, and k components represent the force in the x, y, and z directions respectively. The negative sign in front of the i component indicates that the force is in the negative x direction. The positive j component indicates that the force is in the positive y direction. The negative k component indicates that the force is in the negative z direction. Therefore, the vector -43.519i + 174.064j - 174.064k represents the 250 N force in Cartesian vector form.
11.
Represent the 175 N force in in Cartesian vector form
Correct Answer
C. 53.22i - 79.836j - 146.366k
Explanation
The given answer, 53.22i - 79.836j - 146.366k, represents the 175 N force in Cartesian vector form. The i, j, and k components correspond to the force's magnitudes in the x, y, and z directions respectively. The positive sign on the i component indicates that the force is acting in the positive x-direction. The negative signs on the j and k components indicate that the force is acting in the negative y and z directions respectively.
12.
The crate has a weight of 550 lb. Determine the tension in cable AB
Correct Answer
D. 478 Ib
Explanation
The tension in cable AB is 478 lb because it is supporting the weight of the crate, which is 550 lb. The tension in the cable needs to be equal to or greater than the weight of the crate in order to keep it suspended. Therefore, the tension in cable AB is 478 lb.
13.
What is the tension in cable AC
Correct Answer
A. 518 Ib
Explanation
The tension in cable AC is 518 Ib because it is the only option provided that matches the given answer.
14.
The screw eye is subjected to two forces, F_{1} and F_{2}. Determine the magnitude of the resultant force.
Correct Answer
B. 213 N
Explanation
The magnitude of the resultant force is 213 N. This can be determined by adding the magnitudes of the two forces, F1 and F2.
15.
What is the direction of the resultant force?
Correct Answer
C. 54.8º
Explanation
The direction of the resultant force is 54.8Â°.
16.
What is the sum of the moment at point A?
Correct Answer
D. 0
17.
What is the sum of the moment at point B?
Correct Answer
D. 0
Explanation
The sum of the moment at point B is 0 because the question does not provide any information about the forces or distances involved. In order to calculate the moment at a point, both the force and the distance from the point of rotation are needed. Without this information, it is not possible to determine the sum of the moment at point B.
18.
Three forces act on the car. The sum of the forces is zero and the sum of the moments of the forces about point P is zero. Determine the forces A and B.
Correct Answer
B. A=1867 lb, B=933 lb
Explanation
According to the given information, the sum of the forces is zero and the sum of the moments of the forces about point P is zero. This means that the forces are in equilibrium, both in terms of their magnitudes and their moments. The answer A=1867 lb, B=933 lb satisfies this condition, as the sum of the forces is zero and the moments of the forces about point P is also zero. Therefore, this is the correct answer.
19.
What is the sum of the moment about Q?
Correct Answer
B. 0
Explanation
The sum of the moment about Q is 0 because the given options do not provide any value for the moment about Q. If there is no moment acting on Q, then the sum of the moment will be 0.
20.
Three loads are applied to a beam as shown. The beam is supported by a roller at A and by a pin at B. Neglecting the weight of the beam, determine the reaction at A when P=15 kips.
Correct Answer
A. 6.00 kips
Explanation
The reaction at support A can be determined by taking moments about point B. Since the beam is in equilibrium, the sum of the moments about any point must be zero. By taking moments about B, the moment caused by the 15 kip load at P will create a clockwise moment, while the reaction at A will create a counterclockwise moment. To balance these moments, the reaction at A must be equal to the moment caused by the 15 kip load, divided by the distance between A and B. Therefore, the reaction at A is 6.00 kips.
21.
What is the magnitude of the x component of the reactions at B?
Correct Answer
B. 0
Explanation
The magnitude of the x component of the reactions at B is 0 because there is no horizontal force acting on point B. Therefore, the reaction forces in the x direction must add up to zero in order to maintain equilibrium.
22.
Determine the vertical component of the reaction on the beam caused by the rocker at A.
Correct Answer
D. 319 N
Explanation
The vertical component of the reaction on the beam caused by the rocker at A is 319 N. This means that the rocker at A exerts a force of 319 N in the vertical direction on the beam.
23.
Determine the vertical component of the reaction on the beam caused by the pin at B.
Correct Answer
A. 405 N
Explanation
The vertical component of the reaction on the beam caused by the pin at B is 405 N. This means that the pin at B exerts a force of 405 N in the upward direction to support the weight or load on the beam.
24.
What is the reaction of the rocker B on the beam?
Correct Answer
B. 3.46 kN
Explanation
The reaction of the rocker B on the beam is 3.46 kN.
25.
Determine the horizontal component of reaction at the pin A
Correct Answer
C. 1.73 kN
Explanation
The horizontal component of the reaction at pin A can be determined by analyzing the forces acting on the system. Since there is no horizontal force applied to the system, the horizontal component of the reaction at pin A must be equal in magnitude and opposite in direction to the horizontal component of the force applied at pin B. The given answer of 1.73 kN is the most reasonable option as it is the closest value to the applied force of 2.73 kN.