A student presses a book between his hands, as the drawing indicates. The forces
ID: 1533845 • Letter: A
Question
A student presses a book between his hands, as the drawing indicates. The forces that he exerts on the front and back covers of the book are perpendicular to the book and are horizontal. The book weighs 26.2 N. The coefficient of static friction between his hands and the book is 0.389. To keep the book from falling, what is the magnitude of the minimum pressing force that each hand must exert?
A girl is sledding down a slope that is inclined at 30º with respect to the horizontal. The wind is aiding the motion by providing a steady force of 140 N that is parallel to the motion of the sled. The combined mass of the girl and the sled is 88.1 kg, and the coefficient of kinetic friction between the snow and the runners of the sled is 0.264. How much time is required for the sled to travel down a 221-m slope, starting from rest?
Explanation / Answer
1)
The books weight would be supported half by the front cover, half by the back.
So (26.2N / 2) = 13.1N on each cover.
The force exerted * coefficient of friction = how much downward force it could resist.
X * 0.389 = 13.1N
X = 13.1N / 0.389 = 33.68 (for each hand)
2)
F net = mgsin - µmgcos
F inclined = 88.1*9.81sin 30 - 0.264 *88.1*9.81*cos 30
F inclined = 432.13 - 197.6
F inclined = 234.53 N
Fnet = 234.53 + 140 ( wind ) = 374.53
acceleration = F / m = 374.53 / 88.1 = 4.25 m/s2
e = 1/2 a t ^2
t^2 = 2e / a
t^2 = (221 x 2) / 4.25 = 104
t = 10.2 s
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.