A box of mass m is initially at rest at the highest point of an inclined plane,
ID: 1583357 • Letter: A
Question
A box of mass m is initially at rest at the highest point of an inclined plane, which has a height of 5.9 m and makes an angle of = 15° with respect to the horizontal. After it has been released, you perceive it to be traveling at v = 1 m/s a distance d after the end of the inclined plane as shown. The coefficient of kinetic friction between the box and the plane is p = 0.1, and the coefficient of friction on the horizontal surface is r = 0.2. Find the distance, d, in meters.
HW 7 (Work and Kinetic Energy) Begin Date: 2/27/2018 7:00:00 AM -- Due Date: 3/6/2018 7:00:00 PM End Date: 5/11/2018 11:59:00 PMM (10%) Problem 9: A box of mass m is initially at rest at the highest point of an inclined plane, which has a height of 5.9 m and makes an angle of = 15° with respect to the horizontal. After it has been released, you perceive it to be traveling at 1 m/s a distance d after the end of the inclined plane as shown. The coefficient of kinetic friction between the box and the plane isM,-0.1, and the coefficient of friction on the horizontal surface is , 0.2 initial Final Otheexpertta.com Find the distance d, in meters. Grade Summary Deductions 20% Potential 80% sinO cotanasin0 Submissions Altempts remaining: 8 (10% per attempt) detailed view cosO tan() acos) 1 2 3 atanacotan) sinh() cosh) tnh cotanhO 10% 10% Degrees Radians Submit Hint I give up! Hints: 5% deduction per hint. Hints remaining: 2 Feedback: 0% deduction per feedback.Explanation / Answer
Given,
h = 5.9 m ; theta = 15 deg ; v = 1 m/s
up = 0.1 ; ur = 0.2
We need to find the distance d
from conservation of energy we can write
PE(top) - Wp - Wd = KE
where, PE top is the Potential energy at the top point, Wp is the work done by the frictioanl force on the top, Wd is that on the level surface, KE is the kinetic energy of the box.
m g h - up m g cos(theta) x - ur m g d = 1/2 m v^2
m gets cancelled; using trigonometry, x = h/sin(theta)
9.8 x 5.9 - 0.1 x 9.8 x cos15 x 5.9/sin15 - 0.2 x 9.8 x d = 1/2 x 1^2
d = 18.24 m
Hence, d = 18.24 m
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.