75. T One gallon of paint (volume = 3.79 x 10³ m³) covers an area of 25.0 m². What is the thickness of the fresh paint o
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58. A force F₁ of magnitude 6.00 units acts on an object at the origin in a direction = 30.0° above the positive x-axis (Fig. P1.58). A second force F₂ of magnitude 5.00 units acts on the object in the direction of the positive y-axis. Find graphically the magnitude and direction of the resultant force F₁+F₂. F₁ 0 Figure P1.58
25. The diameter of a sphere is measured to be 5.36 in. Find (a) the radius of the sphere in centimeters, (b) the surface area of the sphere in square centimeters, and (c) the volume of the sphere in cubic centimeters.
Componer 60. Calculate (a) the x-component and (b) the y-component of the vector with magnitude 24.0 m and direction 56.0°.
25. The diameter of a sphere is measured to be 5.36 in. Find (a) the radius of the sphere in centimeters, (b) the surface area of the sphere in square centimeters, and (c) the volume of the sphere in cubic centimeters.
40. A certain corner of a room is selected as the origin of a rectangu- lar coordinate system. If a fly is crawling on an adjacent wall at a point having coordinates (2.0, 1.0), where the units are meters, what is the distance of the fly from the corner of the room?
17. The Roman cubitus is an ancient unit of measure equivalent to about 0.445 m. Convert the 2.00-m height of a basketball forward to cubiti.
8. Use the rules for significant figures to find the answer to the addition problem 21.4 + 15 + 17.17 + 4.003.
6. QC Kinetic energy KE (Topic 5) has dimensions kg. m²/s². It can be written in terms of the momentum p (Topic 6) and mass mas ΚΕ 2m (a) Determine the proper units for momentum using dimen- sional analysis. (b) Refer to Problem 5. Given the units of force, write a simple equation relating a constant force F exerted on an object, an interval of time t during which the force is applied, and the resulting momentum of the object, p.
1. The period of a simple pendulum, defined as the time neces- sary for one complete oscillation, is measured in time units and is given by T= 2T- e g where is the length of the pendulum and g is the accelera- tion due to gravity, in units of length divided by time squared. Show that this equation is dimensionally consistent. (You might want to check the formula using your keys at the end of a string and a stopwatch.) 1 1