What is the tension in the coupling between two trucks on an inclined slope?

  • Thread starter Thread starter xllx
  • Start date Start date
  • Tags Tags
    2d Forces Slope
Click For Summary

Homework Help Overview

The problem involves two trucks, one with a mass of 5kg and the other with a mass of 2kg, being pulled up an inclined slope at 10 degrees. The trucks are connected by a coupling, and the scenario includes forces such as resistance and tension in a pulling string. The objective is to determine the tension in the coupling and to show that it remains in tension regardless of the string's tension.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants discuss the forces acting on each truck, including resistance and gravitational components. There is uncertainty about how to incorporate the tension in the coupling into the equations of motion. Some participants attempt to isolate the second truck to find the tension in the coupling.

Discussion Status

Several participants have shared their calculations and reasoning, with some expressing confusion about the second part of the problem regarding the coupling's tension under different conditions. There is ongoing exploration of the implications of negative tension values and whether they indicate compression or errors in calculations.

Contextual Notes

Participants are working under the constraints of the problem statement and are questioning the assumptions related to the forces acting on the trucks, particularly when considering scenarios with no tension in the string.

xllx
Messages
33
Reaction score
0

Homework Statement


A truck of mass 5kg is pulling a smaller truck of mass 2kg up a slope inclined at 10degrees to the horizontal. The trucks are joined together by a light, rigid coupling. The 5kg truck has a resistance of 8N and the smaller truck has a resistance of 6N. The string pulling the trucks is parallel to the horizontal and has a tension of 43N. The two trucks are accerelerating at 2.5ms-2. What is the tension in the coupling?

Also, show that the coupling remains in tension whatever the tension in the string is.

Homework Equations


F=ma


The Attempt at a Solution


I've drawn a diagram but I am struggling most on which way the tension in the coupling would be so whether to take it away or add it in the Force part of the equation. I've only done the equation for the first truck, but not sure whether it is right:

F=ma
Tension in string- Resistance- Weight component-Tension in coupling= ma
43-8-5(9.8)sin10-T=5x2.5
26.5-T=12.5
T= 14N

I really have no idea for the second part.

Any help at all would be greatly appreciated.
 
Physics news on Phys.org
xllx said:

Homework Statement


A truck of mass 5kg is pulling a smaller truck of mass 2kg up a slope inclined at 10degrees to the horizontal. The trucks are joined together by a light, rigid coupling. The 5kg truck has a resistance of 8N and the smaller truck has a resistance of 6N. The string pulling the trucks is parallel to the horizontal and has a tension of 43N. The two trucks are accerelerating at 2.5ms-2. What is the tension in the coupling?

Also, show that the coupling remains in tension whatever the tension in the string is.

Homework Equations


F=ma

The Attempt at a Solution


I've drawn a diagram but I am struggling most on which way the tension in the coupling would be so whether to take it away or add it in the Force part of the equation. I've only done the equation for the first truck, but not sure whether it is right:

F=ma
Tension in string- Resistance- Weight component-Tension in coupling= ma
43-8-5(9.8)sin10-T=5x2.5
26.5-T=12.5
T= 14N

I really have no idea for the second part.

Any help at all would be greatly appreciated.

Since all they want is tension in the connection to the second truck, then just consider the second truck in isolation.

You have a resistance of 6N, you have a component of gravity m*g*sin10 and you have the additional acceleration that is 2.5m/s2 of the system times its mass.

The sum of those then should be the tension in the coupling between the lead truck that is being pulled with the string and the smaller truck.
 
Thankyou

So would this be right:

F=ma
T-6-2gsin10=2x2.5
T-25.3=5
T=30.3N

Thankyou again.

From that how would I show that the coupling remains in tension no matter what the tension is in the string?
 
xllx said:
Thankyou

So would this be right:

F=ma
T-6-2gsin10=2x2.5
T-25.3=5
T=30.3N

Thankyou again.

From that how would I show that the coupling remains in tension no matter what the tension is in the string?

I would want to check your value for sin10 degrees. (I get .174)

For part 2) consider the case where there is no tension in the string, and the trucks are not accelerating.
 
LowlyPion said:
I would want to check your value for sin10 degrees. (I get .174)
QUOTE]

Sorry, miscalculation. So it would be:
T-9.4=5
T=14.4N

I'm still slightly confused on the second part. When there's no tension in the string, that would mean that it would not be moving up the slope, so the coupling would be in compression and so if a=0, then
F=ma
6+8+2gsin10+5gsin10+T=0
T=-25.9N

Is this anywhere remotely right?
 
xllx said:
I'm still slightly confused on the second part. When there's no tension in the string, that would mean that it would not be moving up the slope, so the coupling would be in compression and so if a=0, then
F=ma
6+8+2gsin10+5gsin10+T=0
T=-25.9N

Is this anywhere remotely right?

Is there a picture with this problem?
 
I've attached a picture, sorry had to draw it on paint.

If the tension in the coupling comes out as a negative does that mean that it is in compresion or just wrong?

thanks
 

Attachments

Similar threads

2 trucks pulling a third truck by the means of a pulley
  • · Replies 24 ·
Replies
24
Views
6K
Mechanics- tension in a coupling
  • · Replies 5 ·
Replies
5
Views
4K
Tension between two objects moving at constant velocity
  • · Replies 3 ·
Replies
3
Views
5K
What is the work done by a tow truck pulling a car 1 km?
  • · Replies 3 ·
Replies
3
Views
5K
Acceleration and Tension in a Two-Block System on an Inclined Plane
  • · Replies 8 ·
Replies
8
Views
2K
What is the largest pulling force before the string breaks?
  • · Replies 13 ·
Replies
13
Views
5K
Tension on a rope between two objects with different mass
  • · Replies 9 ·
Replies
9
Views
43K
Truck and Man Forces in Boat Tension Calculations
  • · Replies 10 ·
Replies
10
Views
2K
What is the tension in a horizontal rope on an inclined plane with friction?
  • · Replies 22 ·
Replies
22
Views
4K
Tension in a string between two blocks
  • · Replies 45 ·
2
Replies
45
Views
24K