# Tention problem

1. Homework Statement
A car acclerates down a hill, going from rest to 22.0m/s in 9.00s. During the acceleration, an object (m=.400kg) hangs by a string from the car's ceiling. The acceleration is such that the string remains perpendicular to the ceiling

Find the angle and the tension in the string

2. Homework Equations

3. The Attempt at a Solution

Could I use these equations?

a=m2gsinθ-m1g/m1+m2

T=m1m2(sinθ+1)/m1+m2

Thank you very much

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Could someone please tell me if these are the correct equations?

Thank you very much

PhanthomJay
Homework Helper
Gold Member
I don't know what you're doing, so check it out: You are given the car's change in speed down the incline over a given time. That is all you need to get its acceleration parallel to the incline. Then draw a free body diagram of the hanging object to solve for your unknowns. Hint: use the slope of the incline as your x axis. Are the object's acceleration and the car's acceleration the same?

Thank you very much

Okay, I know that the car's acceleration=2.444m/s^2 and during the acceleration the string remains perpendicular to the ceiling. When they are perpendicular that's like having i(j), which is 0, right? The free-body-diagram would be a slanted line with a box to represent the car and the string to represent the tention, right? Could you please show me how to find the tention and the angle? The angle shown under the incline would the same as the one with the string, right? I also know that the toy is .400 kg.

Thank you

PhanthomJay
Homework Helper
Gold Member
Thank you very much

Okay, I know that the car's acceleration=2.444m/s^2 and during the acceleration the string remains perpendicular to the ceiling. When they are perpendicular that's like having i(j), which is 0, right? The free-body-diagram would be a slanted line with a box to represent the car and the string to represent the tention, right? Could you please show me how to find the tention and the angle? The angle shown under the incline would the same as the one with the string, right? I also know that the toy is .400 kg.

Thank you
The angle that the string makes with the vertical (theta) is the same as the angle of the incline with respect to the horizontal. Draw a sketch of the object, not the car. There are 2 forces acting on it: its weight, mg, which acts verically down, and the string tension, T, which acts at the angle theta from the vertical. Now determine the net force acting parallel to the incline, and use newton 2. There won't be any "T" component parallel to the incline, so using this one equation will give you theta. Then use newton 1 in the direction perpendicular to the incline to solve for T.

Thank you very much

Regards