1. Force F has a magnitude of 225 N acting at 60° from the horizontal (i.e., the x-axis, 0° on the unit circle). Determine the scalar components of F in the x- and y-directions. A new coordinate system is created by rotating the x- and y-axes 75° counter-clockwise to create the x'- and y'- axes. Determine the scalar components of F in the x' and y' directions.

1. Force F has a magnitude of 225 N acting at 60° from the horizontal (i.e., the x-axis, 0° on the unit circle). Determine the scalar components of F in the x- and y-directions. A new coordinate system is created by rotating the x- and y-axes 75° counter-clockwise to create the x'- and y'- axes. Determine the scalar components of F in the x' and y' directions.

Physics for Scientists and Engineers, Technology Update (No access codes included)

9th Edition

ISBN:9781305116399

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter3: Vectors

Section: Chapter Questions

Problem 3.5CQ

See similar textbooks

Similar questions

A pendulum with a cord of length r = 1.00 m swings in a vertical plane (Fig. P4.42). When the pendulum is in the two horizontal positions = 90.0 and = 270, its speed is 5.00 m/s. Find the magnitude of (a) the radial acceleration and (b) the tangential acceleration for these positions. (c) Draw vector diagrams to determine the direction of the total acceleration for these two positions. (d) Calculate the magnitude and direction of the total acceleration at these two positions. Figure P4.42
In Example 2.6, we considered a simple model for a rocket launched from the surface of the Earth. A better expression for the rockets position measured from the center of the Earth is given by y(t)=(R3/2+3g2Rt)2/3j where R is the radius of the Earth (6.38 106 m) and g is the constant acceleration of an object in free fall near the Earths surface (9.81 m/s2). a. Derive expressions for vy(t) and ay(t). b. Plot y(t), vy(t), and ay(t). (A spreadsheet program would be helpful.) c. When will the rocket be at y=4R? d. What are vy and ay when y=4R?
(a) Show that the rate of change of the free-fall acceleration with vertical position near the Earths surface is dgdr=2GMERE3 This rate of change with position is called a gradient. (b) Assuming h is small in comparison to the radius of the Earth, show that the difference in free-fall acceleration between two points separated by vertical distance h is g=2GMEhRE3 (c) Evaluate this difference for h = 6.00 m, a typical height for a two-story building.
What is the gravitational acceleration close to the surface of a planet with a mass of 2ME and radius of 2RE where ME, and RE are the mass and radius of Earth, respectively? Answer as a multiple of g, the magnitude of the gravitational acceleration near Earths surface. (See Section 7.5.)
A child loves to watch as you fill a transparent plastic bottle with shampoo (Fig P1.65, page 34). Every horizontal cross section of the bottle is circular, but the diameters of the circles have different values. You pour the brightly colored shampoo into the bottle at a constant rate of 16.5 cm3/s. At what rate is its level in the bottle rising (a) at a point where the diameter of the bottle is 6.30 cm and (b) at a point where the diameter is 1.35 cm? Figure P1.65
A car initially traveling eastward turns north by traveling in a circular path at uniform speed as shown in Figure P6.3. The length of the arc ABC is 235 m, and the car completes the turn in 36.0 s. (a) What is the acceleration when the car is at B located at an angle of 35.0? Express your answer in terms of the unit vectors i and j. Determine (b) the cars average speed and (c) its average acceleration during the 36.0-s interval. Figure P6.3
The rectangle shown in Figure P3.56 has sides parallel to the x and y axes. The position vectors of two corners are = 10.0 m at 50.0 and = 12.0 m at 30.0. (a) Find the perimeter of the rectangle. (b) Find the magnitude and direction of the vector from the origin to the upper-right corner of the rectangle.
(a) Calculate the magnitude of the acceleration due to gravity on the surface of Earth due to the Moon. (b) Calculate the magnitude of the acceleration due to gravity at Earth due to the Sun. (c) Take the ratio of the Moon's acceleration to the Sun's and comment on why the tides are predominantly due to the Moon in spite of this number.
Let the four compass directions north, east, south, and west be represented by unit vectors ne . . and respectively. Vertically up and down are represented as u and d. Let us also identify unit vectors that are halfway between these directions such as for northeast. Rank the magnitudes of the following cross products from largest to smallest. If any are equal in magnitude or are equal to zero, show that in your ranking, (a) (b) (c) (d) (e)
Review. Assume a certain liquid, with density 1 230 kg/m3, exerts no friction force on spherical objects. A ball of mass 2.10 kg and radius 9.00 cm is dropped from rest into a deep tank of this liquid from a height of 3.30 m above the surface. (a) Find the speed at which the hall enters the liquid. (b) Evaluate the magnitudes of the two forces that are exerted on the ball as it moves through the liquid. (c) Explain why the ball moves down only a limited distance into the liquid and calculate this distance. (d) With what speed will the ball pop up out of the liquid? (c) How does the time interval tdown, during which the ball moves from the surface down to its lowest point, compare with the lime interval tup for the return trip between the same two points? (f) What If? Now modify the model to suppose the liquid exerts a small friction force on the ball, opposite in direction to its motion. In this case, how do the time intervals tdown and tup compare? Explain your answer with a conceptual argument rather than a numerical calculation.
Saturns ring system forms a relatively thin, circular disk in the equatorial plane of the planet. The inner radius of the ring system is approximately 92,000 km from the center of the planet, and the outer edge is about 137,000 km from the center of the planet. The mass of Saturn itself is 5.68 1026 kg. a. What is the period of a particle in the outer edge compared with the period of a particle in the inner edge? b. How long does it take a particle in the inner edge to move once around Saturn? c. While this inner-edge particle is completing one orbit abound Saturn, how far around Saturn does a particle on the outer edge move?