Question

Now, back to Earth, where there is gravity. A 1 kg book sits on a frictionless inclined plane, tilted at an angle of 30◦ above the horizontal. Hint: If you have trouble with this problem, look at the force diagram you drew for the last problem and rotate it by thirty degrees.

(a) Draw a force diagram for the book.

(b) What are the components of the gravitational force parallel to and perpendicular to the ramp? Draw a right triangle on your force diagram whose hypotenuse is the books weight and the legs are the components, as we usually do. Note that the components will both be diagonal relative to the horizontal/vertical axes.

(c) What magnitude must the normal force have? Remember, the normal force has whatever magnitude that it must have to stop the book from moving “through” the ramp.

(d) What is the acceleration of the book down the ramp? Hint: If you have done the previous problem, this one should be easy; you do not need to show mathematics if you can explain how your answers relate!

Answer 1

b)

parallel Fll = m*g*sin30 = 1*9.8*sin30 = 4.9 N

perpendicular component = m*g*cos30 = 8.5 N

c)

N = 8.5 N

(d)

acclelration a = F/m = 4.9/1 = 4.9 m/s^2