A basket of flowers of mass 3 kg is placed on a flat grassy slope that makes an angle θ with the horizontal. The coefficient of static friction between the basket and the slope is 0.45 and the basket is on the point of slipping down the slope. Model the basket of flowers as a particle and the grassy slope as a plane. Take the magnitude of the acceleration due to gravity, g, to be 9.8 m s−2 . State the forces that act on the basket. Draw a force diagram showing them, defining the symbols that you use to represent the forces and marking the sizes of the angles to show the directions of the forces. Take the unit vector i to point up the slope and the unit vector j to point upwards and perpendicular to the slope. Add these unit vectors to your force diagram.

A particle moving in the xy plane follows a path described as a function of time by i(t) = (3.4 m/s)tî - (2.8 m/s?)tj. A constant force given by F = (5.0î - 2.0j) N acts on the particle (note that other forces must act on the particle as well if it follows the path given above). (a) Determine the displacement of the particle during the interval t = 1.0 s to t = 4.0 s. AT = îm - m (b) Calculate the work done by F during this interval. W =

The force acting on a particle has a magnitude of 110N and is directed 34.4° above the positive x-axis. (a) Determine the x-component of the force. N (b) Determine the y-component of the force. Need Help? Read It

The pelvis P is connected to the femur F at A using three different muscles, which exert the forces shown on the femur. Determine the resultant force and specify its orientation θ, measured counterclockwise from the positive x axis.

A desperate hiker has to think fast to help his friend who has fallen below him. Quickly, he ties m, a rope to a rock of mass m, = 3.90 x 10? kg and makes his way over the ledge (see the figure). If the coefficient of static friction between the rock and the ground is µs = 0.283, and the mass of the hiker is m, = 70.1 kg, what is the maximum mass of the friend m; that the rock can hold so the hikers can then make their way up over the ledge? Assume the rope is parallel to the ground and the point where the rope passes over the ledge is frictionless. kg II

In the figure, a force P acts on a block weighing 45.0 N. The block is initially at rest on a plane inclined at angle = 18.0° to the horizontal. The positive direction of the x axis is up the plane. The coefficients of friction between block and plane are μ = 0.540 and Uk = 0.340. In unit-vector notation, what is the frictional force on the block from the plane when Pis (a) (-5.30 N)î, (b) (-8.10 N)î, and (c) (-15.1 N)? (a) Number i (b) Number i (c) Number i i+ i+ i i i+ i j Units j Units j Units

A block of mass m1 is placed on top of a block of mass m2. You push the two blocks so that they move up a vertical wall, with a constant force of magnitude P directed at angle theta.  The coefficient of friction between m2 and the wall is u. There is no friction between the blocks and no friction between m1 and the wall.  Find the force exerted by the lower block on the upper block.   The answer the book gives me is (P(cos(theta)-u*sin(theta)))/(1+(m2/m1)) I get how to get the numerator but am unsure of how the denominator answer was gotten and where gravity went in the equation

A force P = 873 kN whose line of action passes through points A(1, 1, 4) and B(5, 8, 10). Determine the z-component of force P in kN. Write the numerical value only and in 2 decimal places.

A diving pool that is 4 m deep and full of water has a viewing window on one of its vertical walls. Find the force on a window that is a circle, with a radius of 2 m, tangent to the bottom of the pool. Use 1000 kg/m³ for the density of water and 9.8 m/s² for the acceleration due to gravity. Using the center of the window as the origin, find the width function w(y) for each value of y on the face of the window. w(y) =