# Incline angle for accelerating cart and Tensions in strings for a suspended mass

• JAZZ541
In summary, the first problem involves a trolley with a speed of 20m/s and an acceleration of 4m/s^2 going downhill on a diagonal plane. The slope incline is found to be 23.58°. The second problem involves a weight of 12Kg attached to three strings at a 60° angle with the ceiling, with the tension in each string calculated to be 69.3N.
JAZZ541

## Homework Statement

Hi all, I have solved these problems just wanted to see if it's all ok

problem 1:
a trolley starts at the lowest point of a diagonal plane with a 20m/s speed. Its acceleration is 4m/s^2 going downhill, the trolley goes up then slows until it reaches 0 speed and then goes down the plane with the same acceleration
a. what is the slopes incline? Its is known that the trolley moves without friction?

problem 2:
A weight that has m = 12Kg is pendent in rest on a string attached to two other strings and creating an identical β = 60° with the ceiling, calculate the tension of all strings

## The Attempt at a Solution

solution 1:
[/B]
V0 = 20m/s

a = -4m/s2

g = 10m/s2

m1g • sinα = m1a

N = m1g • cosα

-m1g • sinα = m1a

Sinα = a/-g

Sinα = -4m/s2/-10m/s2

α = 23.58°solution 2:

T1 = mg

m = 12Kg

mg = T1 = 120N

T1 = T2cos30° + T3cos30°

T1 = cos30° • (T2 + T3)

120N = cos30° • (T2 + T3)

T2 + T3 = 120/cos30° = 138.56

T2sin30° = T3sin30°

T2 + T3 = 138.56

2T = 138.56

T2 = T3 = 69.3

TY!

Both solutions look OK.

Ty very much!

## 1. What is the relationship between incline angle and acceleration of a cart?

The incline angle of a ramp affects the acceleration of a cart because it determines the component of the force of gravity acting on the cart. The steeper the incline, the greater the component of gravity pulling the cart down the ramp, resulting in a higher acceleration.

## 2. How do you calculate the tension in a string supporting a suspended mass?

The tension in a string can be calculated using the equation T=mg+ma, where T is the tension, m is the mass of the object, g is the force of gravity, and a is the acceleration of the object. This equation takes into account both the weight of the object and any additional forces acting on it.

## 3. What factors can affect the tension in a string supporting a suspended mass?

The tension in a string can be affected by the mass of the suspended object, the acceleration of the object, and the angle at which the string is suspended. Other factors that can impact tension include the elasticity and strength of the string itself, as well as any external forces acting on the string.

## 4. How does the tension in a string change as the incline angle of a ramp increases?

The tension in a string will increase as the incline angle of a ramp increases. This is because a steeper ramp requires a greater force to keep the object suspended against the pull of gravity. As the incline angle increases, the component of gravity pulling the object down the ramp also increases, leading to a higher tension in the string.

## 5. How does the tension in a string change as the mass of a suspended object increases?

The tension in a string will increase as the mass of a suspended object increases. This is because a heavier object exerts a greater force due to gravity, which must be balanced by the tension in the string. As the mass increases, the tension must also increase to support the weight of the object and maintain its position.

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