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Questions and Answers
A bullet is fired and gets embedded in a block kept on a table. If the table is frictionless, then:
A bomber plane is moving horizontally with a speed of 500m/s and a bomb released from it strikes the ground in 10 seconds. What is the angle at which it strikes the ground, if g = 10m/s²?
A force $F = 3i + cj + 2k$ acting on a particle causes a displacement $S = -4i + 2j + 3k$ in its own direction. If the work done is 6J, then what is the value of c?
The average force necessary to stop a bullet of mass 20g and speed 250 m/s as it penetrates wood to a distance of 12cm is:
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Water falls from a height of 500m. What is the rise in temperature of water at the bottom, if the whole energy remains water? The specific heat of water is 4200 J/kg°C.
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A 7 μF capacitor is charged by a 50V battery. The energy stored in the capacitor is ______.
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Study Notes
Momentum and Energy Conservation
- In a frictionless environment, momentum is conserved when a bullet embeds in a block.
- Kinetic energy is not conserved due to transformation during the embedding process.
- Therefore, momentum gets conserved, while kinetic energy does not.
Projectile Motion of a Bomb
- A bomber plane traveling at 500 m/s releases a bomb that strikes the ground in 10 seconds.
- The angle at which the bomb strikes can be determined using the tangent function.
- With gravitational acceleration (g) set at 10 m/s², the angle of impact is derived from vertical and horizontal motion, leading to option (b) $tan^{-1}(\frac{1}{5})$.
Work-Energy Principle
- A force represented as ( F = 3i + cj + 2k ) acts on a particle causing a displacement ( S = -4i + 2j + 3k ).
- The work done is 6 Joules, allowing calculation of the unknown variable ( c ).
- The work can be found using the dot product of force and displacement vectors; solving gives option (a) ( c = 12 ).
Average Force Calculation
- A bullet with a mass of 20 g (0.02 kg) traveling at 250 m/s penetrates wood to a depth of 12 cm (0.12 m).
- Using equations of motion, calculate the average force needed to stop the bullet.
- The resulting average force is option (a) 5.2 x 10³ N.
Thermal Energy of Falling Water
- Water falls from a height of 500 m, converting potential energy into thermal energy.
- The specific heat capacity of water is 4200 J/kg°C, used to determine temperature rise.
- The calculated increase in temperature at the bottom after falling is option (b) 0.24°C.
Capacitor Charging
- A 7 μF (microfarad) capacitor connected to a 50V battery accumulates charge.
- The capacitance value signifies the capacitor's ability to store electric charge, relevant for direct current (DC) circuits.
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Description
Test your understanding of key physics concepts through practical problems. This quiz covers topics such as momentum conservation and projectile motion. Challenge yourself with real-world scenarios and find out how well you grasp the principles of physics.
