A block with a mass of m = 1.5 kg rests on a wooden plank. The coefficient of static friction between the block and the plank is μs = 0.64. One end of the board is attached to a hinge so that the other end can be lifted forming an angle, θ, with respect to the ground. Assume the x-axis is along the plank as shown in the figure.  a)Assuming the x-direction is along the plank as shown, find an expression for the component of the force of gravity in the y-direction, Fgy, perpendicular to the plank in terms of given quantities and variables available in the palette.  b)Write an expression for the maximum angle, θm, that the board can make with respect to the horizontal before the block starts moving. (Write in terms of the given parameters and variables available in the palette.)  c) Solve numerically for the maximum angle, θm, in degrees.

Three rugby players are pulling horizontally on ropes attached to a box, which remains stationary. Player 1 exerts a force F equal to 200 N at an angle 0, equal to –60.0° with respect to the +x-direction, as shown in the figure. Player 2 exerts a force F2 equal to 300 N at an angle 02 equal to 37.0° with respect to the +x-direction. The view in the figure is from above. Ignore friction and note that gravity can be ignored in this problem. Determine the force F3 exerted by player 3. State your answer by giving the x- and y-components, F3, and Fay, respectively. F, F3x -339.59 N F3y N Player 3's rope breaks, and player 2 adjusts by pulling with a force of magnitude F; equal to 250 N at the same angle as before. Defining angles above the x-axis as positive and those below as negative, at what angle 0 is the acceleration of the box relative to the +x-direction? The magnitude of the acceleration is measured to be 10.0 m/s?. What is the mass m of the box? kg m = F TOOLS x10

Dental braces and kits are used to align and straighten the orientation of the teeth. In a specific case, the tooth that is needed to be aligned is pulled with a force of 9.21 N, 45° CW from the wire (from the +x-axis) and 6.27 N, 45° CCW from the wire (from the +x-axis). What is the magnitude of the resulting force of the two forces aligning the tooth?

Consider a 55-N weight suspended by two wires as shown in the accompanying figure. If the magnitude of vector F₁ is 36 N, find angle a and the magnitude of vector F2. The measure of angle a is (Round to two decimal places as needed.) The magnitude of vector F₂ is N. (Round to two decimal places as needed.) Jα FR 57° (F2

A 20.4 kg mass (m) is suspended by the cable assembly as shown in the figure. The cables have no mass of their own. The cable to the left (T) of the mass makes an angle of 0.00° with the horizontal, and the cable to the right (T2) makes an angle (02) of 30.1°. If the mass is at rest, what is the tension in each of the cables, T and T2? The acceleration due to gravity T, T, is g = 9.81 m/s². N T1 = m N T2 =

In a two-dimensional tug-of-war, Alex, Betty, and Charles pull horizontally on an automobile tire at the angles shown in the picture.

In a two-dimensional tug-of-war, Alex, Betty, and Charles pull horizontally on an automobile tire at the angles shown in the picture. The tire remains stationary in spite of the three pulls. Alex pulls with force É A of magnitude 222 N, and Charles pulls with force magnitude 188 N. Note that the direction of F c is not given. What is the magnitude of Betty's force F B if Charles pulls in (a) the c of direction drawn in the picture or (b) the other possible direction for equilibrium? Alex Charles 140° Betty (a) Number i Units (b) Number i Units

The block shown in (Figure 1) has a mass of m = 75 kg, a height H = 1.1 m, and width L = 1.6 m. It is resting on a ramp that makes an angle 0 = 34° with the horizontal. A force P is applied parallel to the surface of the ramp at the top of the block. What is the maximum force that can be applied without causing the block to move? The coefficient of static friction is μs = 0.42, and the center of mass of the block is at the center of the rectangle. What is the maximum magnitude of P that can be applied before tipping would occur, assuming the block does not slip? Express your answer to three significant figures with appropriate units. Ptip = 649 N Submit Previous Answers Correct Figure W H F x 2 of 2 Part F What is the maximum magnitude of P that does not cause motion of the block? Express your answer to three significant figures with appropriate units. ☐ μÅ Pmax = |667.611 N Submit Previous Answers Request Answer × Incorrect; Try Again; 5 attempts remaining Provide Feedback ? Review…

Three forces are applied to an object, as shown in the figure. Force F₁ has a magnitude of 23.0 newtons (23.0 N) and is directed 30.0° to the left of the +y axis. Force F₂ has a magnitude of 15.0 N and points along the +x axis. What must be the (a) magnitude and (b) direction (specified by the angle in the drawing) of the third force F3 such that the vector sum of the three forces is ON? (a) Number (b) Number i Units Units HE 30.0 F2+5

Vector F1 = 625 N makes an angle of 270 degrees when rotated counterclockwise from the +x axis. Vector F2 = 875 N makes a 120 degree angle from Vector F1 when rotated counterclockwise. What is the direction of the vector needed to balance the two forces?