Help: Kinetic Energy and Friction -- A block pulled by another on a pulley


by aarno
Tags: conservation of ener, friction, kinetics
aarno
aarno is offline
#1
Jul18-10, 04:28 PM
P: 2
In the system the following diagram shows, the block M (mass of 15.65 kg) is initially moving to the left with a speed of 2.26 m/s. The mass of m is 8.26 kg and the coefficients of friction are μs = 0.411 and μk = 0.304. The string is massless and the pulley is massless and frictionless. How fast (m/s) will M be traveling when m has fallen through a height h=2.47 meters?

diagram: http://ce.byu.edu/courses/univ/69482..._blockmass.jpg
Phys.Org News Partner Science news on Phys.org
NASA's space station Robonaut finally getting legs
Free the seed: OSSI nurtures growing plants without patent barriers
Going nuts? Turkey looks to pistachios to heat new eco-city
Doc Al
Doc Al is online now
#2
Jul18-10, 05:10 PM
Mentor
Doc Al's Avatar
P: 40,886
Well, what do you think? What have you done so far?
aarno
aarno is offline
#3
Jul18-10, 06:41 PM
P: 2
^

The pulley makes it so that the second mass exerts a force purely in the x direction, not affecting the normal force. I used left (or down, for the second mass), as the positive direction.
The force exerted by mass m is equal to its mass times gravity, and delta-x equals 2.47 as provided in the problem. Therefore,
W = F * delta-x = (8.26)(9.8)(2.47) = 199.942

The normal force is equal to the weight of mass M, so the force of kinetic friction:
fk = m*g*μk = (15.65)(9.8)(0.304) = 46.6245

Using the following equation, then plugging in the values:
0.5*m*vf^2 = 0.5*m*vf^2 - fk*d + W
0.5*15.65*vf^2 = 0.5*15.65*2.26^2 - 46.6245*2.47 + 199.942

This give vf = 3.993 m/s, while the correct response is 3.49 m/s.

Doc Al
Doc Al is online now
#4
Jul18-10, 06:54 PM
Mentor
Doc Al's Avatar
P: 40,886

Help: Kinetic Energy and Friction -- A block pulled by another on a pulley


Quote Quote by aarno View Post
The force exerted by mass m is equal to its mass times gravity,
That's incorrect. Note that the masses are accelerating. You'll have to solve for the tension in the rope.


Register to reply

Related Discussions
Block pulled at an angle with friction Introductory Physics Homework 4
Block Pulled Up Slope/Coefficient Of Kinetic Friction. Introductory Physics Homework 6
Kinetic friction, pulley, inclined plane Introductory Physics Homework 0
Conservation of energy: Block pulled up frictionless plane Introductory Physics Homework 0
[SOLVED] Mass of a block via kinetic friction Introductory Physics Homework 3