To determine the final velocity of a stone released from the top of a tower, falling freely under the influence of gravity, we can apply principles of kinematics and the laws of motion. Given: - Initial velocity (u) = 0 m/s (as the stone is released from rest) - Height of the tower (s) = 19.6 metersRead more
To determine the final velocity of a stone released from the top of a tower, falling freely under the influence of gravity, we can apply principles of kinematics and the laws of motion.
Given:
– Initial velocity (u) = 0 m/s (as the stone is released from rest)
– Height of the tower (s) = 19.6 meters
– Acceleration due to gravity (g) = 9.81 m/s² (approximately)
Using the equations of motion under constant acceleration, the one relating initial velocity (u), final velocity (v), acceleration (a), and displacement (s) is:
v² = u² + 2as
Here, (v) represents the final velocity, (u) is the initial velocity, (a) is the acceleration due to gravity, and (s) is the displacement (height).
Given that the initial velocity (u) is 0 m/s, the equation simplifies to:
v² = 0 + 2 x 9.81 x 19.6
v² = 0 + 2 x 9.81 x 19.6
v² = 0 + 2 x 192.276
v² = 384.552
Taking the square root of both sides to find (v):
v = √(384.552)
v ≈ 19.6 m/s
Hence, the final velocity of the stone just before touching the ground is approximately 19.6 m/s. This calculation assumes the absence of air resistance or other external forces affecting the stone during its fall.
To determine when and where two stones, one falling from the top of a tower and the other projected vertically upwards from the ground, will meet, we'll apply principles of motion under gravity. Given: - Height of the tower h₁ = 100 meters - Initial velocity of the stone projected upwards (u₁) = 25Read more
To determine when and where two stones, one falling from the top of a tower and the other projected vertically upwards from the ground, will meet, we’ll apply principles of motion under gravity.
Given:
– Height of the tower h₁ = 100 meters
– Initial velocity of the stone projected upwards (u₁) = 25 m/s
– Acceleration due to gravity g = 9.81 m/s² (approximately)
Calculating time for the stone projected upwards to reach maximum height:
Using the equation (v = u + at) where (v) is the final velocity, (u) is the initial velocity, (a) is the acceleration due to gravity, and (t) is time:
At maximum height, the final velocity (v) becomes (0 m/s) momentarily before the stone starts falling back down. So, v = 0, u = 25 m/s, and a = -9.81m/s² (negative due to opposing the upward motion).
v = u + at
0 = 25 – 9.81t
t = 25/9.81
t ≈ 2.55 seconds
Calculating the height reached by the stone projected upwards after 2.55 seconds:
The height (s₂) reached by the stone is calculated using the equation (s = ut + 1/2 at² ):
s₂ = u₁t + 1/2 gt²
s₂ = 25 x 2.55 +1/2 x (-9.81) \times (2.55)²
s₂ ≈ 63.75 meters
Therefore, after approximately 2.55 seconds, the stone projected upwards reaches a height of approximately 63.75 meters.
Conclusion:
Both stones will meet after 2.55 seconds at a height of approximately 63.75 meters above the ground.
When an object is immersed in a liquid, it experiences an upward force known as the buoyant force. This force acts in the upward direction, perpendicular to the surface of the liquid at any given point within the liquid. Here are some key points about the direction of the buoyant force: 1. Upward DiRead more
When an object is immersed in a liquid, it experiences an upward force known as the buoyant force. This force acts in the upward direction, perpendicular to the surface of the liquid at any given point within the liquid.
Here are some key points about the direction of the buoyant force:
1. Upward Direction: The buoyant force always acts in the upward direction when an object is submerged in a liquid. It opposes the force of gravity that pulls the object downward.
2. Result of Pressure Differences: The buoyant force arises due to differences in pressure within the liquid. As an object is submerged, the pressure at the bottom is higher than at the top, resulting in a net upward force.
3. Equal to Displaced Liquid: According to Archimedes’ principle, the buoyant force is equal to the weight of the liquid displaced by the immersed object. It is this displaced liquid that exerts an upward force on the object.
4. Determines Buoyancy: The direction and magnitude of the buoyant force are key in determining the buoyancy of an object. If the buoyant force is greater than the object’s weight, it floats; if it’s less, the object sinks; and if it’s equal, the object remains suspended in the liquid.
In summary, the buoyant force always acts in the upward direction when an object is immersed in a liquid. This force is a consequence of the pressure differences within the liquid and plays a significant role in determining whether an object will float, sink, or remain suspended in the liquid.
When a block of plastic is released underwater, it ascends to the surface due to the fundamental principles of buoyancy and density. Here's a breakdown of why this happens: 1. Buoyant Force: When an object is submerged in a fluid, it experiences an upward force known as the buoyant force. This forceRead more
When a block of plastic is released underwater, it ascends to the surface due to the fundamental principles of buoyancy and density.
Here’s a breakdown of why this happens:
1. Buoyant Force: When an object is submerged in a fluid, it experiences an upward force known as the buoyant force. This force is equal to the weight of the fluid displaced by the object.
2. Density Difference: Plastic typically has a lower density compared to water. Density signifies how much mass is packed into a certain volume. Since the density of plastic is less than that of water, the plastic block is less dense than the water it displaces.
3. Archimedes’ Principle: This principle states that the buoyant force acting on an object is equivalent to the weight of the fluid it displaces. If the buoyant force is greater than the weight of the object, the object will float or rise.
4. Resultant Force: Given that the plastic block is less dense than water, the buoyant force acting on it is greater than its own weight. Consequently, there is an overall upward force, propelling the block upwards through the water until it reaches the water’s surface.
In essence, the block of plastic ascends to the surface because its density is lower than that of water, resulting in a stronger upward buoyant force as per Archimedes’ principle. This disparity in density causes the plastic block to float and rise towards the water’s surface when submerged.
Force = Mass x Acceleration Given: - Mass of the vehicle (m) = 1500 kg - Negative acceleration (a) = -1.7 m/s² (negative because it's slowing down) Substituting the values into the formula: Force = 1500 kg x -1.7m/s² Force = -2550N The negative sign indicates that the force is acting in the oppositeRead more
Force = Mass x Acceleration
Given:
– Mass of the vehicle (m) = 1500 kg
– Negative acceleration (a) = -1.7 m/s² (negative because it’s slowing down)
Substituting the values into the formula:
Force = 1500 kg x -1.7m/s²
Force = -2550N
The negative sign indicates that the force is acting in the opposite direction to the motion of the vehicle, which is required to cause the negative acceleration (deceleration) and eventually stop the vehicle.
A stone is released from the top of a tower of height 19.6 m. Calculate its final velocity.
To determine the final velocity of a stone released from the top of a tower, falling freely under the influence of gravity, we can apply principles of kinematics and the laws of motion. Given: - Initial velocity (u) = 0 m/s (as the stone is released from rest) - Height of the tower (s) = 19.6 metersRead more
To determine the final velocity of a stone released from the top of a tower, falling freely under the influence of gravity, we can apply principles of kinematics and the laws of motion.
Given:
– Initial velocity (u) = 0 m/s (as the stone is released from rest)
– Height of the tower (s) = 19.6 meters
– Acceleration due to gravity (g) = 9.81 m/s² (approximately)
Using the equations of motion under constant acceleration, the one relating initial velocity (u), final velocity (v), acceleration (a), and displacement (s) is:
v² = u² + 2as
Here, (v) represents the final velocity, (u) is the initial velocity, (a) is the acceleration due to gravity, and (s) is the displacement (height).
Given that the initial velocity (u) is 0 m/s, the equation simplifies to:
v² = 0 + 2 x 9.81 x 19.6
v² = 0 + 2 x 9.81 x 19.6
v² = 0 + 2 x 192.276
v² = 384.552
Taking the square root of both sides to find (v):
v = √(384.552)
v ≈ 19.6 m/s
Hence, the final velocity of the stone just before touching the ground is approximately 19.6 m/s. This calculation assumes the absence of air resistance or other external forces affecting the stone during its fall.
See lessA stone is allowed to fall from the top of a tower 100 m high and at the same time another stone is projected vertically upwards from the ground with a velocity of 25 m/s. Calculate when and where the two stones will meet.
To determine when and where two stones, one falling from the top of a tower and the other projected vertically upwards from the ground, will meet, we'll apply principles of motion under gravity. Given: - Height of the tower h₁ = 100 meters - Initial velocity of the stone projected upwards (u₁) = 25Read more
To determine when and where two stones, one falling from the top of a tower and the other projected vertically upwards from the ground, will meet, we’ll apply principles of motion under gravity.
Given:
– Height of the tower h₁ = 100 meters
– Initial velocity of the stone projected upwards (u₁) = 25 m/s
– Acceleration due to gravity g = 9.81 m/s² (approximately)
Calculating time for the stone projected upwards to reach maximum height:
Using the equation (v = u + at) where (v) is the final velocity, (u) is the initial velocity, (a) is the acceleration due to gravity, and (t) is time:
At maximum height, the final velocity (v) becomes (0 m/s) momentarily before the stone starts falling back down. So, v = 0, u = 25 m/s, and a = -9.81m/s² (negative due to opposing the upward motion).
v = u + at
0 = 25 – 9.81t
t = 25/9.81
t ≈ 2.55 seconds
Calculating the height reached by the stone projected upwards after 2.55 seconds:
The height (s₂) reached by the stone is calculated using the equation (s = ut + 1/2 at² ):
s₂ = u₁t + 1/2 gt²
s₂ = 25 x 2.55 +1/2 x (-9.81) \times (2.55)²
s₂ ≈ 63.75 meters
Therefore, after approximately 2.55 seconds, the stone projected upwards reaches a height of approximately 63.75 meters.
Conclusion:
See lessBoth stones will meet after 2.55 seconds at a height of approximately 63.75 meters above the ground.
In what direction does the buoyant force on an object immersed in a liquid act?
When an object is immersed in a liquid, it experiences an upward force known as the buoyant force. This force acts in the upward direction, perpendicular to the surface of the liquid at any given point within the liquid. Here are some key points about the direction of the buoyant force: 1. Upward DiRead more
When an object is immersed in a liquid, it experiences an upward force known as the buoyant force. This force acts in the upward direction, perpendicular to the surface of the liquid at any given point within the liquid.
Here are some key points about the direction of the buoyant force:
1. Upward Direction: The buoyant force always acts in the upward direction when an object is submerged in a liquid. It opposes the force of gravity that pulls the object downward.
2. Result of Pressure Differences: The buoyant force arises due to differences in pressure within the liquid. As an object is submerged, the pressure at the bottom is higher than at the top, resulting in a net upward force.
3. Equal to Displaced Liquid: According to Archimedes’ principle, the buoyant force is equal to the weight of the liquid displaced by the immersed object. It is this displaced liquid that exerts an upward force on the object.
4. Determines Buoyancy: The direction and magnitude of the buoyant force are key in determining the buoyancy of an object. If the buoyant force is greater than the object’s weight, it floats; if it’s less, the object sinks; and if it’s equal, the object remains suspended in the liquid.
In summary, the buoyant force always acts in the upward direction when an object is immersed in a liquid. This force is a consequence of the pressure differences within the liquid and plays a significant role in determining whether an object will float, sink, or remain suspended in the liquid.
See lessWhy does a block of plastic released under water come up to the surface of water?
When a block of plastic is released underwater, it ascends to the surface due to the fundamental principles of buoyancy and density. Here's a breakdown of why this happens: 1. Buoyant Force: When an object is submerged in a fluid, it experiences an upward force known as the buoyant force. This forceRead more
When a block of plastic is released underwater, it ascends to the surface due to the fundamental principles of buoyancy and density.
Here’s a breakdown of why this happens:
1. Buoyant Force: When an object is submerged in a fluid, it experiences an upward force known as the buoyant force. This force is equal to the weight of the fluid displaced by the object.
2. Density Difference: Plastic typically has a lower density compared to water. Density signifies how much mass is packed into a certain volume. Since the density of plastic is less than that of water, the plastic block is less dense than the water it displaces.
3. Archimedes’ Principle: This principle states that the buoyant force acting on an object is equivalent to the weight of the fluid it displaces. If the buoyant force is greater than the weight of the object, the object will float or rise.
4. Resultant Force: Given that the plastic block is less dense than water, the buoyant force acting on it is greater than its own weight. Consequently, there is an overall upward force, propelling the block upwards through the water until it reaches the water’s surface.
In essence, the block of plastic ascends to the surface because its density is lower than that of water, resulting in a stronger upward buoyant force as per Archimedes’ principle. This disparity in density causes the plastic block to float and rise towards the water’s surface when submerged.
See lessAn automobile vehicle has a mass of 1500 kg. What must be the force between the vehicle and road if the vehicle is to be stopped with a negative acceleration of 1.7 m s–2?
Force = Mass x Acceleration Given: - Mass of the vehicle (m) = 1500 kg - Negative acceleration (a) = -1.7 m/s² (negative because it's slowing down) Substituting the values into the formula: Force = 1500 kg x -1.7m/s² Force = -2550N The negative sign indicates that the force is acting in the oppositeRead more
Force = Mass x Acceleration
Given:
– Mass of the vehicle (m) = 1500 kg
– Negative acceleration (a) = -1.7 m/s² (negative because it’s slowing down)
Substituting the values into the formula:
Force = 1500 kg x -1.7m/s²
Force = -2550N
The negative sign indicates that the force is acting in the opposite direction to the motion of the vehicle, which is required to cause the negative acceleration (deceleration) and eventually stop the vehicle.
See less