Online Quiz On Mechanics

The magnitude of the resultant force is 213 N. This can be determined by adding the magnitudes of the two forces, F1 and F2.

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.

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.

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(25°) = 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(25°) = 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.

The coordinate direction angle β 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 β would be 0°. Therefore, the given answer of 60° is incorrect.

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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.

The direction of the resultant force is 54.8°.

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.

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.

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.

The direction measured clockwise from the x-axis is 103°.

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.

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.

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.

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.

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.

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.

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.

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.

The reaction of the rocker B on the beam is 3.46 kN.

The tension in cable AC is 518 Ib because it is the only option provided that matches the given answer.

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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.

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.