Confusion about work done by friction as negative or positive

In summary, when two blocks are released from a table with a kinetic friction coefficient of .3, the speed of the blocks at the instant they hit the floor is 4.29 m/s.
  • #1
kjamha
98
1
https://lh3.googleusercontent.com/0GOyZeQMdpLgYxYwwP4FMabe-Mk7QpADPC4ZK4PVpBGKvamcqjopOf3M0evdhE8PHZ3iTQ=s138 m1 is 4 kg and m2 is 8 kg. The kinetic friction coefficient on the table is 0.3. m1 is held in place. When m1 is released, m2 accelerates 1.2 m to the floor. Use conservation of energy/ and or Work KE principle to find the speed of the two blocks at the instant m2 hits the floor.

I used the following equation to solve the problem:

PE = KE1 + KE2 + work(friction) with g = 10 m/s2

8x10x1.2 = 1/2 (4) (v2) + 1/2 (8) (v2) + Nx.3x1.2 and then solved for v.

I got the right answer but I see work done by friction as negative (the force and displacement are in opposite directions). If I use a negative number here, I get the wrong answer. Also, regarding conservation of energy, I see a change in PE as negative energy (decrease in PE), the friction as negative work and the change in KE for m1 and m2 as a gain in energy. Shouldn't the change in PE + work done by friction = change in KE of m1 + change in KE of m2? Why is work done by friction positive in my original equation?
 
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  • #2
You've got the sign of Wf wrong. How did you arive at this equation? Because when non conservative forces are present, ΔΕ=W, where W is the work of the non conservative forces. ΔΕ=K1+K2-P0, so P0=K1+K2-Wf.
 
  • #3
Another method giving the same result is this:
ΔΚ=Wf+Wg
Wg=-ΔP=P0
P0=K1+K2-Wf
 
  • #4
Your equation makes sense to me. Plugging in numbers for P0=K1+K2-Wf (using g = 10m/s2):
96 = 4v2 + 2v2 - 0.03x40x1.2
96 + 14.4 = 6v2
v = 4.29 m/s
If friction is eliminated, then 96 = 4v2 + 2v2 and v = 4 m/s. This is slower than 4.29. Adding friction should slow down the speed. That is why added Wf, which gives me the correct answer. I like your equations, but why is it giving me the wrong answer?
 
  • #5
P0+Wf=K (where K=K1+K2), and since friction does a negative work, if you remove it, K is larger.
 
  • #6
I see it. Thanks!
 
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Likes Andreas C

FAQ: Confusion about work done by friction as negative or positive

1. Why is work done by friction sometimes considered negative?

Friction is often considered negative because it opposes the motion of an object and therefore decreases its kinetic energy. This means that the work done by friction results in a decrease in the overall energy of the system.

2. How can work done by friction be positive?

In some cases, work done by friction can actually be considered positive. For example, when a car's brakes are applied, the friction between the brake pads and the wheels causes the car to slow down and eventually stop. This can be seen as a positive change in the car's motion, as it is necessary for safe driving.

3. Can friction ever be considered both negative and positive?

Yes, in certain situations, the work done by friction can be both negative and positive. For instance, when a ball rolls down a hill, friction between the ball and the ground will slow it down, resulting in negative work done. However, if the same ball is then launched up a hill using a slingshot, the force of friction between the ball and the slingshot will do positive work by accelerating the ball in the opposite direction.

4. How does the direction of motion affect the work done by friction?

The direction of motion does not have a direct effect on the work done by friction. Friction always acts in the opposite direction of an object's motion, regardless of the direction. However, the sign of the work done by friction will depend on the direction of the force applied.

5. Why is it important to understand the concept of work done by friction?

Understanding the concept of work done by friction is essential in many real-life situations, such as driving a car, riding a bike, or even walking. It allows us to predict and control the motion of objects, as well as make informed decisions about the materials and surfaces we use in our daily lives. Additionally, understanding friction can also lead to the development of more efficient and durable machines and technologies.

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