Tension/acceleration between 2 Masses

  • Thread starter tascja
  • Start date
In summary: Now check the next part.In summary, two masses, m1 = 1.5 kg and m2 = 3 kg, are connected by a string running over a massless pulley. M1 slides on a 35-degree ramp with a coefficient of kinetic friction of 0.40, while m2 hangs from the string. The question is asking for the acceleration of the masses. To solve this problem, analyze the forces acting on each mass separately using Newton's 2nd law. The net force equation for m1 is Fnet = ma, which can be rewritten as ma = T - (downsloping component of gravity) - Ff. To solve for T, isolate it and substitute it into
  • #1
tascja
87
0

Homework Statement


two masses are connected by a thing string running over a massless pulley. m1 slides on a 35deg ramp with a coefficient of kinetic friction of 0.40, while m2 hans from the string. what is the acceleration of the masses?
m1 = 1.5 kg
m2 = 3 kg

Homework Equations


Fnet = ma

The Attempt at a Solution


im not quite sure how to relate the object that is on an incline to the object that is hanging and has its forces going up and down?

would the net force equation just be:
Fnet = (m1+m2)a
m2g - Ff - T = (m1 +m2)a
 
Physics news on Phys.org
  • #2
Rather than attempt to treat both masses together in one equation from the outset, analyze the forces acting on each mass separately. Apply Newton's 2nd law to each, then combine the two equations to solve for the acceleration.
 
  • #3
m2g - Ff - T = (m1 +m2)a
You wouldn't put in the Tension when including all the forces like this. Tension is put in when you use separate equations for each mass.

You do have another force to add to Ff acting on m1 - the component of the force of gravity that is acting down the ramp.
 
  • #4
Doc Al said:
Rather than attempt to treat both masses together in one equation from the outset, analyze the forces acting on each mass separately. Apply Newton's 2nd law to each, then combine the two equations to solve for the acceleration.
when you say combine do you mean equate or add the two equations??
Here i equated by isolating T and substituting into the other equation.

so for mass1:
Fnet = ma
ma = T-(downsloping component of gravity) - Ff
= T- 14.7sin35 - 5.88
T = (1.5)a +2.55

for mass2:
Fnet = ma
mg - T = ma
T = mg - ma
T = 29.4 - 3a

then:

29.4 - 3a = (1.5)a + 2.55
a = 5.97 m/s^2

does that seem right?
 
  • #5
tascja said:
when you say combine do you mean equate or add the two equations??
I just meant solve them simultaneously. There are several ways to do that. (Adding them to eliminate T might be the easiest.)
Here i equated by isolating T and substituting into the other equation.
Perfectly fine.

so for mass1:
Fnet = ma
ma = T-(downsloping component of gravity) - Ff
Good.
= T- 14.7sin35 - 5.88
T = (1.5)a +2.55
How did you solve for the friction?

for mass2:
Fnet = ma
mg - T = ma
T = mg - ma
T = 29.4 - 3a
Good.

then:

29.4 - 3a = (1.5)a + 2.55
a = 5.97 m/s^2

does that seem right?
Right idea, but check your numbers.
 
  • #6
How did you solve for the friction?
** sorry i don't know where i got 5.88 from?? but i think it should be:
in the question it told me that the coefficient of friction is 0.40.
Ff = μFn

Fn = 14.7cos35
= 12.04 N

Ff = (12.04)(0.4)
= 4.816 N
 
  • #7
tascja said:
** sorry i don't know where i got 5.88 from?? but i think it should be:
in the question it told me that the coefficient of friction is 0.40.
Ff = μFn

Fn = 14.7cos35
= 12.04 N

Ff = (12.04)(0.4)
= 4.816 N
Much better.
 

1. What is tension?

Tension is a force that is transmitted through a medium, such as a rope or cable, when it is pulled tight by forces acting on each end. It is a reaction force that occurs when an object is stretched or pulled.

2. How is tension calculated?

Tension can be calculated using the formula T = mg, where T is the tension force, m is the mass of the object, and g is the acceleration due to gravity. This formula assumes that the object is not accelerating and is in a state of equilibrium.

3. How does tension affect acceleration between two masses?

Tension can affect the acceleration between two masses in different ways. If the tension force is greater than the force of gravity pulling the masses down, it can cause the masses to accelerate upwards. On the other hand, if the tension force is less than the force of gravity, the masses will accelerate downwards. In both cases, the tension force is a factor in determining the acceleration of the masses.

4. Can tension be negative?

No, tension cannot be negative. It is always a positive value, as it is a reaction force to an applied force. However, tension can have a direction, which can be either upwards or downwards, depending on the direction of the applied force.

5. How can tension be measured?

Tension can be measured using a device called a dynamometer, which is designed specifically for measuring tension forces. This device works by applying a force to a spring and measuring the amount of stretch, which is directly proportional to the tension force. Another way to measure tension is by using a scale or balance, which can determine the weight of an object being pulled by a tension force.

Similar threads

  • Introductory Physics Homework Help
Replies
3
Views
703
  • Introductory Physics Homework Help
Replies
5
Views
1K
  • Introductory Physics Homework Help
Replies
23
Views
1K
  • Introductory Physics Homework Help
Replies
10
Views
2K
  • Introductory Physics Homework Help
Replies
33
Views
2K
  • Introductory Physics Homework Help
Replies
2
Views
793
Replies
25
Views
2K
  • Introductory Physics Homework Help
Replies
3
Views
1K
  • Introductory Physics Homework Help
Replies
4
Views
893
  • Introductory Physics Homework Help
Replies
16
Views
1K
Back
Top