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A bullet of mass 10g travelling horizontally at a velocity of 150 m/s strikes a stationary wooden block and comes to rest in 0.03 s. Calculate the distance of penetration of the bullet into the block. Also calculate the magnitude of the force exerted by the wooden block on the bullet?
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A bullet of mass 10g travelling horizontally at a velocity of 150 m/s ...
Calculation of Distance of Penetration
To determine the distance of penetration of the bullet into the wooden block, we can use the kinematic equation:
\[
s = ut + \frac{1}{2} a t^2
\]
Where:
- \( s \) = distance of penetration
- \( u \) = initial velocity of the bullet = 150 m/s
- \( t \) = time taken to come to rest = 0.03 s
- \( a \) = acceleration
First, we need to calculate the acceleration (\( a \)). Since the bullet comes to rest, its final velocity (\( v \)) is 0 m/s. We can use the formula:
\[
a = \frac{v - u}{t}
\]
Substituting the values:
\[
a = \frac{0 - 150}{0.03} = -5000 \, \text{m/s}^2
\]
Now, substituting the values into the distance formula:
\[
s = 150 \times 0.03 + \frac{1}{2} \times (-5000) \times (0.03)^2
\]
\[
s = 4.5 - 2.25 = 2.25 \, \text{meters}
\]
Thus, the distance of penetration of the bullet into the block is 2.25 meters.
Magnitude of the Force Exerted by the Block
The force exerted by the wooden block on the bullet can be calculated using Newton's second law:
\[
F = ma
\]
Where:
- \( F \) = force
- \( m \) = mass of the bullet = 10 g = 0.01 kg
- \( a \) = acceleration = -5000 m/s² (magnitude will be considered)
Substituting the values:
\[
F = 0.01 \times 5000 = 50 \, \text{N}
\]
Hence, the magnitude of the force exerted by the wooden block on the bullet is 50 N.
To determine the distance of penetration of the bullet into the wooden block, we can use the kinematic equation:
\[
s = ut + \frac{1}{2} a t^2
\]
Where:
- \( s \) = distance of penetration
- \( u \) = initial velocity of the bullet = 150 m/s
- \( t \) = time taken to come to rest = 0.03 s
- \( a \) = acceleration
First, we need to calculate the acceleration (\( a \)). Since the bullet comes to rest, its final velocity (\( v \)) is 0 m/s. We can use the formula:
\[
a = \frac{v - u}{t}
\]
Substituting the values:
\[
a = \frac{0 - 150}{0.03} = -5000 \, \text{m/s}^2
\]
Now, substituting the values into the distance formula:
\[
s = 150 \times 0.03 + \frac{1}{2} \times (-5000) \times (0.03)^2
\]
\[
s = 4.5 - 2.25 = 2.25 \, \text{meters}
\]
Thus, the distance of penetration of the bullet into the block is 2.25 meters.
Magnitude of the Force Exerted by the Block
The force exerted by the wooden block on the bullet can be calculated using Newton's second law:
\[
F = ma
\]
Where:
- \( F \) = force
- \( m \) = mass of the bullet = 10 g = 0.01 kg
- \( a \) = acceleration = -5000 m/s² (magnitude will be considered)
Substituting the values:
\[
F = 0.01 \times 5000 = 50 \, \text{N}
\]
Hence, the magnitude of the force exerted by the wooden block on the bullet is 50 N.
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A bullet of mass 10g travelling horizontally at a velocity of 150 m/s strikes a stationary wooden block and comes to rest in 0.03 s. Calculate the distance of penetration of the bullet into the block. Also calculate the magnitude of the force exerted by the wooden block on the bullet?
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A bullet of mass 10g travelling horizontally at a velocity of 150 m/s strikes a stationary wooden block and comes to rest in 0.03 s. Calculate the distance of penetration of the bullet into the block. Also calculate the magnitude of the force exerted by the wooden block on the bullet? for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about A bullet of mass 10g travelling horizontally at a velocity of 150 m/s strikes a stationary wooden block and comes to rest in 0.03 s. Calculate the distance of penetration of the bullet into the block. Also calculate the magnitude of the force exerted by the wooden block on the bullet? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A bullet of mass 10g travelling horizontally at a velocity of 150 m/s strikes a stationary wooden block and comes to rest in 0.03 s. Calculate the distance of penetration of the bullet into the block. Also calculate the magnitude of the force exerted by the wooden block on the bullet?.
A bullet of mass 10g travelling horizontally at a velocity of 150 m/s strikes a stationary wooden block and comes to rest in 0.03 s. Calculate the distance of penetration of the bullet into the block. Also calculate the magnitude of the force exerted by the wooden block on the bullet? for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about A bullet of mass 10g travelling horizontally at a velocity of 150 m/s strikes a stationary wooden block and comes to rest in 0.03 s. Calculate the distance of penetration of the bullet into the block. Also calculate the magnitude of the force exerted by the wooden block on the bullet? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A bullet of mass 10g travelling horizontally at a velocity of 150 m/s strikes a stationary wooden block and comes to rest in 0.03 s. Calculate the distance of penetration of the bullet into the block. Also calculate the magnitude of the force exerted by the wooden block on the bullet?.
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