Question

In: Physics

A 45.0-kg crate is dragged at constant velocity 8.20 m across a horizontal floor with a...

A 45.0-kg crate is dragged at constant velocity 8.20 m across a horizontal floor with a rope making a 30 degree angle above the horizontal. The coefficient of kinetic friction is 0.250. Find the work done by friction. Give your answer in Joules.

Solutions

Expert Solution

as given the crate is dragged at constant velocity the net force acting on it is zero.
lets talk about the forces in horizontal plane first,
the horizontal component of the tension(T) in the rope(i.e.Tcos30) is equal to the frictional force which is acting in the opposite direction.
the tricky part here is to calculate the frictional force,it will not be simply calculated as (0.25)(45)(9.8),,
because there is a vertical component of the tension(Tsin30) in the rope which is reducing the effective weight of the crate,which is (45*9.8)-Tsin30.
Thus,the force of friction=(0.25)[(45*9.8)-Tsin30]
this is equated against the horizontal component of the tension in the rope(i.e.Tcos30).
we get,Tcos30=(0.25)[(45*9.8)-Tsin30]
Tcos30=(0.25)[441-T/2]
on solving you get T=111.3N.
the work done by rope is force*displacement*cos30
=111.3*(8.2)*(cos30)
=790joules.


the work done by friction is frictional force*displacement*cos180(since the direction of force is opposite to the direction of displacement)
as already stated the frictional force is equal to the horizontal component of tension(Tcos30),the answer becomes


=111.3(cos30)*(8.2)*cos180 (cos180=-1) = -790joules
the work done is in negative since the direction of force is opposite to the direction of displacement.

45.0-kg crate is dragged at constant velocity 8.20 m across a horizontal floor with a rope making a 30 degree angle above the horizontal. The coefficient of kinetic friction is 0.250

work done by friction = Ffr x d =

-?(9.81)45 x 8.2 = -904.9725 Joules

work done by rope = F?? x 8.2

F?? = Ffr ------------------------> [since the object is at constant velocity , a = 0 => F(resultant) = 0]

= (0.25)45(9.81) = 110.3625 N

=> work done by rope = 110.3625 x 8.2 = 904.9725 J

net work done = 904.9725 - 904.9725 = 0


Related Solutions

A 91 kg crate, starting from rest, is pulled across a floor with a constant horizontal...
A 91 kg crate, starting from rest, is pulled across a floor with a constant horizontal force of 340 N . For the first 15m the floor is frictionless, and for the next 15 m the coefficient of friction is 0.22. What is the final speed of the crate?
A 107-kg crate is being pushed across a horizontal floor by a force P that makes...
A 107-kg crate is being pushed across a horizontal floor by a force P that makes an angle of 18.5 ° below the horizontal. The coefficient of kinetic friction is 0.246. What should be the magnitude of P, so that the net work done by it and the kinetic frictional force is zero?
A 102-kg crate is being pushed across a horizontal floor by a force P that makes...
A 102-kg crate is being pushed across a horizontal floor by a force P that makes an angle of 41.7 ° below the horizontal. The coefficient of kinetic friction is 0.232. What should be the magnitude of P, so that the net work done by it and the kinetic frictional force is zero?
Elmer Fudd pulls a 65.0 kg wooden crate of mass m across the floor with a...
Elmer Fudd pulls a 65.0 kg wooden crate of mass m across the floor with a force F at an angle of 34.0°. The coefficient of friction between the surfaces is m = 0.235. If the crate moves at a constant speed, what is the magnitude of the applied force F?
A 40-kg crate that is pushed at constant velocity a distance 10.0 m along a 30°...
A 40-kg crate that is pushed at constant velocity a distance 10.0 m along a 30° incline by the horizontal force F. The coefficient of kinetic friction between the crate and the incline is µk = 0.30. a.)Calculate the work done by the applied force. b.)Calculate the work done by the frictional force.
Work on a sliding crate. A worker pushes a 47.0 Kg crate across a level horizontal...
Work on a sliding crate. A worker pushes a 47.0 Kg crate across a level horizontal floor by applying a constant force of exactly 150.0 N at an angle of 23.0 degrees below the horizontal. The crate begins at rest and ends 15.0m from where it started traveling at 2.6m/s A. What is the work done by the applied force as the crate moves across the floor? B What is the work done by the friction force as the crate...
A 1,300-N crate is being pushed across a level floor at a constant speed by a...
A 1,300-N crate is being pushed across a level floor at a constant speed by a force F of 390 N at an angle of 20.0° below the horizontal, as shown in the figure a below. Two figures show a side view of a crate positioned upon a horizontal surface. Figure (a): An arrow pointing downward and to the right is labeled vector F and forms an angle of 20° below the horizontal as it approaches the upper left edge...
A 45 kg wooden crate is being pushed across a wooden floor with a force of...
A 45 kg wooden crate is being pushed across a wooden floor with a force of 175 N. If, uk = 0.03. What is the acceleration of the crate?
9.) A 19.6 kg block is dragged over a rough, horizontal surface by a constant force...
9.) A 19.6 kg block is dragged over a rough, horizontal surface by a constant force of 183 N acting at an angle of angle 30.5 ◦ above the horizontal. The block is displaced 97.1 m and the coefficient of kinetic friction is 0.121. a. Find the work done by the normal force. Answer in units of J. b. What is the net work done on the block? Answer in units of J.
A man pulls a crate of mass 61.0 kg across a level floor. He pulls with...
A man pulls a crate of mass 61.0 kg across a level floor. He pulls with a force of 180.0 N at an angle of 29.0° above the horizontal. When the crate is moving, the frictional force between the floor and the crate has a magnitude of 122.0 N. If the crate starts from rest, how fast will it be moving after the man has pulled it a distance of 2.50 m?
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT