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Questions and Answers
What is the acceleration of two masses, 5 kg and 4.8 kg, hanging over a light frictionless pulley? (g = 9.8 m/s²)
What is the acceleration of two masses, 5 kg and 4.8 kg, hanging over a light frictionless pulley? (g = 9.8 m/s²)
- 9.8 m/s²
- 5 m/s²
- 4.8 m/s²
- 0.2 m/s² (correct)
What is the weight of a 500 gm mass thrown with a speed of 20 m/s on planet X?
What is the weight of a 500 gm mass thrown with a speed of 20 m/s on planet X?
- 104 N
- 1 N
- None of these
- 10 N (correct)
What happens to the component of weight parallel to an inclined plane as it is made horizontal?
What happens to the component of weight parallel to an inclined plane as it is made horizontal?
- Decreases (correct)
- Remains the same
- Increases
- First increases then decreases
What does an elevator experience if the tension in its cable equals its weight?
What does an elevator experience if the tension in its cable equals its weight?
What is the maximum acceleration a 30 kg monkey can achieve when climbing a rope that withstands a maximum tension of 360 N? (g = 10 m/s²)
What is the maximum acceleration a 30 kg monkey can achieve when climbing a rope that withstands a maximum tension of 360 N? (g = 10 m/s²)
When is the apparent weight of a body in an elevator greater than its weight at rest?
When is the apparent weight of a body in an elevator greater than its weight at rest?
Momentum is most closely related to which of the following?
Momentum is most closely related to which of the following?
If two forces have a sum of 18 N and are perpendicular, what is the magnitude of their resultant force if it is 12 N?
If two forces have a sum of 18 N and are perpendicular, what is the magnitude of their resultant force if it is 12 N?
What is the upward acceleration of an elevator weighing 5000 kg with a tension of 50000 N in the cable?
What is the upward acceleration of an elevator weighing 5000 kg with a tension of 50000 N in the cable?
What is the coefficient of friction when a force of 49 N is required to pull a 10 kg block on a rough surface?
What is the coefficient of friction when a force of 49 N is required to pull a 10 kg block on a rough surface?
What is not required for a body to maintain uniform velocity?
What is not required for a body to maintain uniform velocity?
If a block with a mass of 10 kg is on a rough horizontal surface with a coefficient of friction of 0.5, what is the acceleration when a horizontal force of 100 N is applied?
If a block with a mass of 10 kg is on a rough horizontal surface with a coefficient of friction of 0.5, what is the acceleration when a horizontal force of 100 N is applied?
Which option accurately calculates the tension developed in a lift of mass 1000 kg moving upward with an acceleration of $1 m/s^2$? (Use $g = 10 m/s^2$)
Which option accurately calculates the tension developed in a lift of mass 1000 kg moving upward with an acceleration of $1 m/s^2$? (Use $g = 10 m/s^2$)
What is the angle of inclination when a block starts to slide down an inclined plane with a coefficient of friction of µ = 0.5?
What is the angle of inclination when a block starts to slide down an inclined plane with a coefficient of friction of µ = 0.5?
When a ball moving with a momentum of 15 kgm/s strikes a wall at 30° and reflects at the same angle, what is the change in momentum?
When a ball moving with a momentum of 15 kgm/s strikes a wall at 30° and reflects at the same angle, what is the change in momentum?
What happens to the tension exerted by the surface of the lift if the rope of the lift breaks suddenly?
What happens to the tension exerted by the surface of the lift if the rope of the lift breaks suddenly?
While a man is hanging on a spring balance in an ascending lift, what would happen to the reading of the balance?
While a man is hanging on a spring balance in an ascending lift, what would happen to the reading of the balance?
If a man weighing 80 kg stands on a scale in a lift accelerating upwards at $5 m/s^2$, what will the scale read? (Use $g = 10 m/s^2$)
If a man weighing 80 kg stands on a scale in a lift accelerating upwards at $5 m/s^2$, what will the scale read? (Use $g = 10 m/s^2$)
What is the stopping distance if a car traveling at $120 km/h$ is initially able to stop within $20 m$ at $60 km/h$?
What is the stopping distance if a car traveling at $120 km/h$ is initially able to stop within $20 m$ at $60 km/h$?
If a body has constant momentum, what must also be constant?
If a body has constant momentum, what must also be constant?
Which principle does the motion of a rocket primarily rely on?
Which principle does the motion of a rocket primarily rely on?
What is the resultant force when two forces of 5 N each act along the x and y axes?
What is the resultant force when two forces of 5 N each act along the x and y axes?
If the angle between two forces is 120 degrees and their magnitudes are 10 N and 5 N respectively, what is the resulting acceleration of a 2 kg mass?
If the angle between two forces is 120 degrees and their magnitudes are 10 N and 5 N respectively, what is the resulting acceleration of a 2 kg mass?
What can be concluded when the vector sum of two forces is perpendicular to their vector differences?
What can be concluded when the vector sum of two forces is perpendicular to their vector differences?
In the expression for linear momentum p(t) = Aicos(kt) - jsin(kt), what is the resultant angle between the force and momentum?
In the expression for linear momentum p(t) = Aicos(kt) - jsin(kt), what is the resultant angle between the force and momentum?
If two blocks with masses 5 kg and 2 kg are connected by a string and a vertical force F is applied, what is the value of F if the tension in the string is 40 N?
If two blocks with masses 5 kg and 2 kg are connected by a string and a vertical force F is applied, what is the value of F if the tension in the string is 40 N?
What will be the ratio of masses m1 and m2 if the acceleration of two bodies is g/7?
What will be the ratio of masses m1 and m2 if the acceleration of two bodies is g/7?
What would be the tension in the string between the first two blocks if three identical blocks of mass 2 kg each are accelerated by a force of 10.2 N?
What would be the tension in the string between the first two blocks if three identical blocks of mass 2 kg each are accelerated by a force of 10.2 N?
What is the acceleration of a 5 kg block sliding down a frictionless inclined plane at an angle of 30 degrees to the horizontal?
What is the acceleration of a 5 kg block sliding down a frictionless inclined plane at an angle of 30 degrees to the horizontal?
What is the coefficient of static friction for a block that begins to move with a force of 25 N acting on it, given its weight is 100 N?
What is the coefficient of static friction for a block that begins to move with a force of 25 N acting on it, given its weight is 100 N?
A block moving at 10 m/s comes to rest in 25.5 m. What is the deceleration experienced by the block?
A block moving at 10 m/s comes to rest in 25.5 m. What is the deceleration experienced by the block?
What is the frictional force on a block that is being pulled with a force of 0.1 N but does not move?
What is the frictional force on a block that is being pulled with a force of 0.1 N but does not move?
If a force of 50 N is applied to a body of mass 20 kg moving initially at 15 m/s, how long will it take to stop?
If a force of 50 N is applied to a body of mass 20 kg moving initially at 15 m/s, how long will it take to stop?
What should be the value of a force F applied at an angle of 30° to move a block with a static friction coefficient of 0.25?
What should be the value of a force F applied at an angle of 30° to move a block with a static friction coefficient of 0.25?
During which condition will the reading on a weighing scale in a lift show zero?
During which condition will the reading on a weighing scale in a lift show zero?
If a force of 6 N acts on a body of mass 1 kg at rest, causing it to attain a velocity of 30 m/s, how long does this force act?
If a force of 6 N acts on a body of mass 1 kg at rest, causing it to attain a velocity of 30 m/s, how long does this force act?
For a block lying on an inclined plane with a weight of 50 N, if the inclination angle is 30°, how would the weight affect the motion of the block?
For a block lying on an inclined plane with a weight of 50 N, if the inclination angle is 30°, how would the weight affect the motion of the block?
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Study Notes
Forces and Motion
- A force is unnecessary to maintain uniform velocity; hence no force is needed when speed remains constant.
- Acceleration of a lift affects tension; a 1000 kg lift with 1 m/s² upward acceleration develops tension of 10800 N.
- When a lift cable breaks, tension becomes zero as there’s no upward force.
- When a man hangs in a rising lift, a spring balance shows increased reading due to upward acceleration.
Weight and Acceleration
- A man weighing 80 kg in a lift moving upward with 5 m/s² has scale reading of 1200 N when considering gravitational force as 10 m/s².
- An automobile's braking distance increases with the square of speed; doubling speed from 60 km/h to 120 km/h can increase stopping distance to 80 m.
Momentum and Energy Principles
- Constant momentum implies constant velocity, as constant momentum dictates zero net force.
- Rocket motion is based on the conservation of linear momentum.
- The recoil of a 5 kg bullet shot from a 5 kg gun at 500 m/s generates a recoil velocity of 0.5 m/s, showcasing conservation of momentum.
Acceleration in Pulley Systems
- The acceleration of two hanging masses (3 kg and 4 kg) in a pulley system is 4.9 m/s² due to gravitational force.
- Acceleration of two masses tied through a massless pulley relies on gravitational force and additional input; with 5 kg and 4.8 kg, acceleration is 0.2 m/s².
Impulse and Friction
- The impulse required to stop a 1500 kg car traveling at 90 km/h is -37500 Ns, illustrating momentum change necessity.
- Coefficient of friction with a force of 49 N pulling a 10 kg block equals 0.5, demonstrating frictional limits on rough surfaces.
Static and Dynamic Situations
- Weighing scales show varying readings in elevators depending on motion; readings change when accelerating up or down.
- A static equilibrium requires a force greater than friction to initiate motion; static friction's coefficient ranges based on surface and weight.
Practical Examples in Mechanics
- For a 5 kg and 2 kg block system, applied force F of 140 N results in a tension of 40 N in the connector string.
- On an inclined surface, a 5 kg block experiences accelerations of 4.9 m/s² (frictionless) or 3.2 m/s² (with kinetic friction).
Real-life Applications
- Accelerating a block of mass 10 kg with a force of 100 N results in an acceleration of 5 m/s² on a rough surface.
- A 75 kg man in a lift moving upwards with 2 m/s² encounters a normal force of 900 N acting on him.
Calculating Force and Motion Dynamics
- Distance to acquire speed from rest is derived using friction coefficients; e.g., min distance for a car starting from rest to reach 72 km/h is 40 m.
- The angle at which a block starts sliding down an inclined plane can be determined through static friction analysis, yielding 30° for values given.
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