# Calculate acceleration of the system

• briiannnaa04
In summary, a 28.0 kg block is connected to an empty 1 kg bucket by a cord running over a frictionless pulley. The coefficient of static friction between the table and block is 0.320. Sand is gradually added to the bucket until the system just begins to move. The mass of sand added to the bucket can be calculated using the sum of forces = ma and Ff=uFn equations. The forces acting on the bucket include gravity and the tension in the cord, while the block has gravity, friction, and tension in the cord. The tension in the cord is equal to the gravitational force on the bucket, and when the tension is equal to the force of friction, the system will start moving.
briiannnaa04

## Homework Statement

A 28.0 kg block is connected to an empty 1 kg bucket by a cord running over a frictionless pulley. The coefficient of static friction between the table and block is 0.320. Sand is gradually added to the bucket until the system just begins to move. a) calculate the mass of sand added to bucket. b) Calculate acceleration of the system

Sum of forces=MA
Ff=uFn

## The Attempt at a Solution

You are supposed to write up your attempt - surely you have something, perhaps the diagram of forces or equations for the sum of forces = ma on each object.

i really don't know how to start it, i drew a diagram but I am not sure what to do next

What forces act on the bucket?
What forces act on the block?

gravity and the normal force
The normal force, gravity, friction?

The bucket has gravity acting on it and the tension in the cord. The block has gravity, friction and the tension in the cord. The tensions in the cord are THE SAME.

When the tension in the cord is equal to the force of friction ANY SECOND after this the system is going to start moving. Is there any way you can define the tension in the cord using the forces on either the bucket or the block?

Great - you are started! Now use the two formulas you listed.

Tension in the cord on the bucket is equal to the gravitational force?

Yes, the tension in the cord is equal to the gravitational force of the bucket. Both tensions are the same.

## 1. What is acceleration?

Acceleration is the rate of change of an object's velocity over time. It is a vector quantity, meaning it has both magnitude and direction.

## 2. How is acceleration calculated?

Acceleration can be calculated by dividing the change in velocity by the change in time. The formula for acceleration is a = (vf - vi) / t, where vf is the final velocity, vi is the initial velocity, and t is the time interval.

## 3. What units is acceleration measured in?

Acceleration is typically measured in meters per second squared (m/s²) in the SI system. Other common units include centimeters per second squared (cm/s²) and kilometers per hour squared (km/h²).

## 4. What factors affect the acceleration of a system?

The acceleration of a system can be affected by various factors, such as the mass of the object, the force applied to the object, and any external forces acting on the system. The direction of the force also plays a role in determining the acceleration.

## 5. How can acceleration be used in real-world applications?

Acceleration is a crucial concept in many real-world applications, such as predicting the motion of objects in sports, designing vehicles and machines, and understanding the behavior of celestial bodies in space. It is also used in everyday scenarios, such as calculating the acceleration of a car during braking or a roller coaster during a loop.

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