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A bullet of mass 10g travelling horizontally with a velocity of 150ms−1 strikes a stationary wooden block and come to rest in 0.03s. 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)120 N
- b)50 N
- c)- 50 N
- d)- 120 N
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
A bullet of mass10gtravelling horizontally with a velocity of150ms&min...
- Initial velocity of the bullet, u = 150 m/s
- Final velocity of the bullet, v = 0
- Mass of the bullet, m = 10 g = 0.01 kg
- Time taken by the bullet to come to rest, t = 0.03 s
- Let the distance of penetration be s
Using the first equation of motion:
v = u + at
Substituting the known values:
0 = 150 + a(0.03)
⇒ a = -5000 m/s² (Negative sign indicates retardation)
v = u + at
Substituting the known values:
0 = 150 + a(0.03)
⇒ a = -5000 m/s² (Negative sign indicates retardation)
Now using the second equation of motion:
v² = u² + 2as
Substituting the known values:
0 = 150² + 2 × (-5000) × s
⇒ s = 2.25 m (Distance of penetration)
v² = u² + 2as
Substituting the known values:
0 = 150² + 2 × (-5000) × s
⇒ s = 2.25 m (Distance of penetration)
Magnitude of the force exerted by the wooden block:
Using |F| = m|a|
|F| = 0.01 × 5000 = 50 N
Using |F| = m|a|
|F| = 0.01 × 5000 = 50 N
So, the force exerted by the wooden block is 50 N.
Community Answer
A bullet of mass10gtravelling horizontally with a velocity of150ms&min...
Given Data
- Mass of the bullet (m) = 10 g = 0.01 kg (converted to kg)
- Initial velocity of the bullet (u) = 150 m/s
- Final velocity of the bullet (v) = 0 m/s (comes to rest)
- Time taken to come to rest (t) = 0.03 s
Distance of Penetration
To find the distance (s) the bullet penetrates into the block, we can use the formula:
s = ut + (1/2)at^2
First, we need to calculate the acceleration (a) using the formula:
a = (v - u) / t
- a = (0 - 150) / 0.03 = -5000 m/s² (negative indicates deceleration)
Now, substitute the values into the distance formula:
s = (150)(0.03) + (1/2)(-5000)(0.03)^2
Calculating step-by-step:
- s = 4.5 - (1/2)(5000)(0.0009)
- s = 4.5 - 2.25 = 2.25 m
Magnitude of Force
To find the force (F) exerted by the wooden block on the bullet, we use Newton's second law:
F = ma
- F = (0.01 kg)(-5000 m/s²) = -50 N
The negative sign indicates that the force exerted is in the opposite direction of the bullet's motion.
Final Results
- Distance of penetration: 2.25 m
- Magnitude of force exerted: 50 N
Thus, the correct answer is option 'B': 2.25 m, 50 N.
- Mass of the bullet (m) = 10 g = 0.01 kg (converted to kg)
- Initial velocity of the bullet (u) = 150 m/s
- Final velocity of the bullet (v) = 0 m/s (comes to rest)
- Time taken to come to rest (t) = 0.03 s
Distance of Penetration
To find the distance (s) the bullet penetrates into the block, we can use the formula:
s = ut + (1/2)at^2
First, we need to calculate the acceleration (a) using the formula:
a = (v - u) / t
- a = (0 - 150) / 0.03 = -5000 m/s² (negative indicates deceleration)
Now, substitute the values into the distance formula:
s = (150)(0.03) + (1/2)(-5000)(0.03)^2
Calculating step-by-step:
- s = 4.5 - (1/2)(5000)(0.0009)
- s = 4.5 - 2.25 = 2.25 m
Magnitude of Force
To find the force (F) exerted by the wooden block on the bullet, we use Newton's second law:
F = ma
- F = (0.01 kg)(-5000 m/s²) = -50 N
The negative sign indicates that the force exerted is in the opposite direction of the bullet's motion.
Final Results
- Distance of penetration: 2.25 m
- Magnitude of force exerted: 50 N
Thus, the correct answer is option 'B': 2.25 m, 50 N.
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