A block of mass M rests on a plane inclined at angle θ. You apply a horizontal force of F = Mg to the block towards the inclined plane. Assume that the friction force between the block and plane is large enough to keep the block still. What are the normal and friction forces (call them N and Ff ) that the plane exerts on the block?

We will break the forces up into components parallel and perpendicular to the plane (ˆx and ˆy coordinates would work just as well). The forces are F = Mg, Ff , N, and the weight Mg. Balancing the forces parallel and perpendicular to the plane gives, respectively (with upward along the plane taken to be positive), Ff = Mg sin θ − Mg cos θ, and N = Mg cos θ + Mg sin θ.

A radio station tower was built in two sections. From a point 87 feet from the base of the tower, the angle of elevation of the top of the first section is 25º, and the angle of elevation of the top of the second section is 40º. To the nearest foot, what is the height of the top section of the tower?

Think of this problem as working with two separate triangles: (1) the larger triangle with the 40 degrees angle and a vertical side that represents the entire height, b, of the tower, and (2) the smaller triangle with the 25 degrees angle and a vertical side, a, that represents the height of the first (bottom) section of the tower. Solve for the vertical heights (b and a) in the two separate triangles. The needed height, x, of the second (top) section of the tower will be the difference between the ENTIRE height, b, and the height of the first (bottom) section, a. You will need to subtract. In both triangles, the solution deals with "opposite" and "adjacent" making it a tangent problem. Larger triangle with height b: tan(40)=b/87 Which gives b=73.00166791 Smaller triangle with height a: tan(25)=a/87 Which gives a=40.56876626 Difference (b - a): 73.00166791 - 40.56876626 = 32.43290165 = 32 feet(approx)

How much current flows through a 40W light bulb, assuming that the voltage is 120V. How much would it cost to have the light on for one year 24/7?

Power equals voltage times current. So, 40W = 120V * I I = 40W / 120V I = 0.3 Amps So your lightbulb uses 300 milli-amps of current. If you want to know the cost of your light bulb, you can calculate that using just power. 1 kilowatt hour is equal 1000 watts of power being consumed for the duration of 1 hour. A 40W lightbulb would take 25 hours to consume 1 kWh. Since 40W * 25h = 1000 Watt-hours So if you take a dollar and divide by 0.12074 and multiply by 25 hours then you will find out a 40W lightbulb cost 1 dollar if you leave it on for 207 hours, which is about 8.6 days.