Tension of Rope, Friction, And Work Done

In summary, a man is dragging a 25.0kg crate across the floor with a rope, facing a coefficient of kinetic friction of 0.250. The tension in the rope is 200.0 N at a 30.0° angle to the vertical. To find the net work done on the box as it travels 10.0 m, the tension force was broken into x and y components and the frictional force was calculated. The normal force and weight are not the same and the net force in the x direction should be used to find the new angle. The formula W= F x distance x cos theta can be used to calculate the work done, and it was found to be 820 Joules.
  • #1
Extremist223
7
0
A man drags a 25.0kg crate, by a rope, across the floor whose coefficient of kinetic friction is 0.250. The tension in the rope is 200.0 N at an angle of 30.0° to the vertical. What is the net work done on the box as it travels 10.0 m?


well I broke the tension force into the x and y components with, these equations.
cos60x200 = 100N
sin60x200=173.205N
also the Frictional force in the opposite direction of +x movement is fk=ukFN
fk= 0.25 x 25kg x 9.8m/s^2 = 61.25N

This is where I'm stuck, I thought I could subtract the x components and create a new triangle, find the new angle and determine the work done with W= Force x Distance cos theta. The answer I'm getting seems to be wrong.

Please answer this as soon as possible, I have a midterm tommorow and I'm struggling to teach myself. Thank you.
 
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  • #2
oh I finally got it, I was forgetting that the y comp of tension was making the object lighter, so the answer is 820 Joules.
 
  • #3
Extremist223 said:
A man drags a 25.0kg crate, by a rope, across the floor whose coefficient of kinetic friction is 0.250. The tension in the rope is 200.0 N at an angle of 30.0° to the vertical. What is the net work done on the box as it travels 10.0 m?


well I broke the tension force into the x and y components with, these equations.
cos60x200 = 100N
sin60x200=173.205N
OK,(100 N is the x component, and 173 N up is the y component)
Frictional force in the opposite direction of +x movement is fk=ukFN
fk= 0.25 x 25kg x 9.8m/s^2 = 61.25N
The Normal force and the weight are not the same. Sum forces in y direction to find it.
This is where I'm stuck, I thought I could subtract the x components and create a new triangle,
rather, you should find the net force in the x direction
find the new angle and determine the work done with W= Force x Distance cos theta. The answer I'm getting seems to be wrong.

Please answer this as soon as possible, I have a midterm tommorow and I'm struggling to teach myself. Thank you.
try using W_net = F_x(net) times distance. Is there any F_net in the y direction?
 

FAQ: Tension of Rope, Friction, And Work Done

What is tension and how does it affect a rope?

Tension is the force that is exerted on a rope when it is pulled at both ends. It is a measure of the internal forces within the rope that keep it from breaking or stretching. The higher the tension, the tighter the rope will be, and the more difficult it will be to stretch or break.

What is friction and how does it impact the tension of a rope?

Friction is the force that resists the motion of two surfaces that are in contact with each other. In the context of a rope, friction plays a role in determining the tension. If there is a lot of friction between the rope and the surface it is resting on, the tension will be greater as the rope will be more difficult to move. On the other hand, if there is less friction, the tension will be lower.

How is work done on a rope?

Work done on a rope is the product of the force applied to the rope and the distance over which the force is applied. In other words, if you pull on a rope and move it a certain distance, you are doing work on the rope. The amount of work done will depend on the magnitude of the force and the distance moved.

Can the tension of a rope change over time?

Yes, the tension of a rope can change over time. This can happen if the force applied to the rope changes or if the rope itself stretches or wears out. For example, if you gradually pull on a rope with increasing force, the tension will also increase. Similarly, if the rope is exposed to harsh weather conditions or is used frequently, it may stretch or weaken, resulting in a decrease in tension.

How can we calculate the tension in a rope?

The tension in a rope can be calculated using the equation T = F/a, where T is the tension, F is the force applied to the rope, and a is the cross-sectional area of the rope. This equation is based on Hooke's law which states that the tension in an ideal rope is directly proportional to the force applied to it. However, in real-life situations, the tension may also be affected by factors such as friction and the weight of the rope itself.

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