what is the TENSION IN THE STRING A BLOCC PUT INSIDE THE WATER DENSITY OF BLOCK LESSTHEN THE DENSITY OF LIQUID,THE CONTAINER MOVING UPWORDS

To understand the tension in the string when a block is submerged in a liquid with a density less than that of the block, while the container is moving upwards, we need to consider several physical principles, including buoyancy, tension, and the effects of acceleration.

Key Concepts to Consider

Let's break down the situation step by step:

• Density and Buoyancy: The density of the block is greater than that of the liquid, which means that the block will tend to sink. However, the liquid exerts an upward buoyant force on the block, which is equal to the weight of the liquid displaced by the block.
• Weight of the Block: The weight of the block can be calculated using the formula: Weight = mass × gravity (W = mg).
• Tension in the String: The tension in the string will depend on the net forces acting on the block, which include the weight of the block, the buoyant force, and any additional forces due to the upward acceleration of the container.

Analyzing the Forces

When the container moves upwards, it accelerates, which affects the forces acting on the block. The effective weight of the block increases due to this upward acceleration. We can express the forces acting on the block as follows:

• The weight of the block (downward): W = mg
• The buoyant force (upward): F_b = ρ_liquid × V_displaced × g, where ρ_liquid is the density of the liquid and V_displaced is the volume of the block submerged.
• The effective weight due to upward acceleration (a): W_effective = m(g + a)

Calculating Tension

The tension in the string can be derived from the balance of forces acting on the block. The equation can be set up as follows:

T - F_b = W_effective

Rearranging this gives us:

T = W_effective + F_b

Substituting the expressions we have:

T = m(g + a) + ρ_liquid × V_displaced × g

Example Calculation

Let’s say we have a block with a mass of 2 kg, the density of the liquid is 800 kg/m³, and the block is submerged in a volume of 0.002 m³. If the container accelerates upwards at 2 m/s², we can calculate the tension:

• Weight of the block: W = 2 kg × 9.81 m/s² = 19.62 N
• Buoyant force: F_b = 800 kg/m³ × 0.002 m³ × 9.81 m/s² = 15.696 N
• Effective weight: W_effective = 2 kg × (9.81 m/s² + 2 m/s²) = 23.62 N

Now, substituting these values into the tension equation:

T = 23.62 N + 15.696 N = 39.316 N

Conclusion

The tension in the string holding the block will be approximately 39.32 N when the container is moving upwards with an acceleration of 2 m/s². This example illustrates how the interplay of buoyancy, weight, and acceleration affects the tension in the string. Understanding these principles can help you analyze similar problems in physics effectively.