Net Work Done on an Object by 3 Forces

In summary, the net work done on the canister by the three forces during the first 6.80 m of displacement is 33.4403 J. This was found by finding the x components of F2 and F3, subtracting them, and then using Pythagorean theorem to find the overall force. However, it was incorrect to assume that F1 and the difference of F2 and F3 formed a 90 degree angle. The problem is best solved by adding force components in the x and y directions, and then converting to polar coordinates as needed.
  • #1
TheSnacks
6
0

Homework Statement



Figure 7-30 shows an overhead view of three horizontal forces acting on a cargo canister that was initially stationary but that now moves across a frictionless floor. The force magnitudes are F1 = 2.70 N, F2 = 5.31 N, and F3 = 9.69 N, and the indicated angles are θ2 = 50.8° and θ3 = 39.6°. What is the net work done on the canister by the three forces during the first 6.80 m of displacement?


Homework Equations



I didn't really use equations other than things that are obvious.

W = Fd


The Attempt at a Solution



I found the x components of F2 and F3 and got 3.35608 and 7.46627 respectively. Since they are opposite of each other, I found the difference which was 4.11019.

Then, since it seems as though F1 and the difference of F2 and F3 forms a 90 degree angle, I used Pythagorean theorem to find the overall force. That came out to be 4.91769.

I plugged it into W=Fd and got 33.4403.

I'm not sure where I went wrong. Any help would be appreciated.
 
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  • #2
Without a diagram, it's a little hard to check your work. Can you attach a PDF or JPEG of your problem?
 
  • #3
  • #4
TheSnacks said:

Homework Statement



Figure 7-30 shows an overhead view of three horizontal forces acting on a cargo canister that was initially stationary but that now moves across a frictionless floor. The force magnitudes are F1 = 2.70 N, F2 = 5.31 N, and F3 = 9.69 N, and the indicated angles are θ2 = 50.8° and θ3 = 39.6°. What is the net work done on the canister by the three forces during the first 6.80 m of displacement?


Homework Equations



I didn't really use equations other than things that are obvious.

W = Fd


The Attempt at a Solution



I found the x components of F2 and F3 and got 3.35608 and 7.46627 respectively. Since they are opposite of each other, I found the difference which was 4.11019.

Then, since it seems as though F1 and the difference of F2 and F3 forms a 90 degree angle, I used Pythagorean theorem to find the overall force. That came out to be 4.91769.

I plugged it into W=Fd and got 33.4403.

I'm not sure where I went wrong. Any help would be appreciated.

Theta 2 and theta 3 are not opposite. Does that help?

This type of problem is usually best done by adding force components in the x and y directions (rectangular coordinates). After you get the resultant force vector in rectangular coordinates, you can convert that to polar coordinates (magnitude and direction) if needed, as it is in this problem.
 

1. What is net work done on an object by 3 forces?

The net work done on an object by 3 forces is the total amount of work done on the object by all three forces combined. This can be calculated by adding the individual work done by each force.

2. How do you calculate net work done on an object by 3 forces?

To calculate net work done on an object by 3 forces, you need to find the work done by each individual force using the formula W = Fd (work = force x distance). Then, add these individual work values to get the total net work done.

3. Can the net work done on an object by 3 forces be negative?

Yes, the net work done on an object by 3 forces can be negative if the forces are acting in opposite directions. In this case, the work done by one force can cancel out the work done by another force, resulting in a negative net work value.

4. Does the direction of the forces affect the net work done on an object?

Yes, the direction of the forces does affect the net work done on an object. If the forces are acting in the same direction, the net work will be positive. If the forces are acting in opposite directions, the net work will be negative.

5. Can the net work done on an object by 3 forces be zero?

Yes, the net work done on an object by 3 forces can be zero if the forces are balanced and cancel each other out. This means that the work done by one force is equal in magnitude and opposite in direction to the work done by the other forces, resulting in a net work value of zero.

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