Calculate the work done by friction of package

In summary, the conversation discusses a 5.00 kg package sliding down a 1.50 m ramp inclined at 12 degrees below horizontal with a coefficient of kinetic friction of 0.310. The work done by friction, gravity, and the net work done on the package are calculated, and the final speed is determined if the package starts with an initial speed of 2.2 m/s. The equations used include Fk = n * coefficient, W = Fd cos angle, and K= 1/2 mv^2. There is a difference of opinion on whether to break down forces into x and y components, but the original solution is deemed correct.
  • #1
veronicak5678
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Homework Statement



A 5.00 kg package slides 1.50 m down a ramp that is inclined at 12 degrees below horizontal. The coefficient of kinetic friction is 0.310.
a- Calculate the work done by friction.
b- Calculate the work done by gravity.
c- Determine the net work done on package.
d- If thepackage started sliding with a speed of 2.2 m/s, find the final speed.

Homework Equations



Fk = n * coefficient
W = Fd cos angle
K= i/2 mv^2

The Attempt at a Solution



a-
n (Normal) = wcos 12= 47.9 N
Fk (Friction) = normal * coefficient = 14.8N
Work Fk = 1.5m * 14.8 N * cos 180 = -22.2 J

b-
wsin12 * 1.5m * cos 0 = 15.3 J

c-
W total = 15.3J - 22.2 J = -6.9 J

d-
1/2 m v init ^2 - 6.9 J = 1/2 m vfinal ^2

12.1 J - 6.9 J = 2.5 kg v final ^2

v final = 1.44 m/s


I was feeling pretty good about this, but I showed it to someone in my school's math lab and he told me he thought it was all wrong. He said I need to break every force in x and y components. I don't see why I would. I would appreciate it if someone could tell me if I am doing this correctly.
 
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  • #2
You are correct.
 
  • #3
Alright! Thank you.
 

1. How do you calculate the work done by friction of a package?

To calculate the work done by friction, you need to know the coefficient of friction, the force applied to the package, and the distance the package travels due to friction. The formula for calculating work is work = force x distance. Once you have all the necessary information, simply plug it into the formula to find the work done by friction.

2. What is the coefficient of friction?

The coefficient of friction is a measure of how much resistance there is between two surfaces in contact with each other. It is represented by the symbol "μ" and is typically listed in tables for different materials. It is a dimensionless quantity and is used to calculate the force of friction.

3. How does friction affect the work done by a package?

Friction is a force that opposes motion between two surfaces in contact with each other. As a package moves, friction will act in the opposite direction of its motion, slowing it down. This means that friction will decrease the amount of work done by the package, as some of the force applied is used to overcome the frictional force.

4. Can the work done by friction be negative?

Yes, the work done by friction can be negative. If the package is moving in the opposite direction of the applied force, then the work done by friction will be in the opposite direction as well. This means that the work done by friction is negative, indicating that the package is losing energy due to friction.

5. How does the weight of the package affect the work done by friction?

The weight of the package does not directly affect the work done by friction. However, a heavier package will have a greater force of gravity acting on it, which will increase the force needed to move the package. This means that more work will be required to overcome the frictional force, resulting in a larger amount of work done by friction.

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