Bullet B weighs 0.5 oz and blocks A and C both weigh 3 lb. The coefficient of friction between the blocks and the plane is μk = 0.25. Initially, the bullet is moving at v0 and blocks A and C are at rest (Fig. 1). After the bullet passes through A, it becomes embedded in block C and all three objects come to stop in the positions shown (Fig. 2). Determine the initial speed of the bullet v0.
Fig. P13.149
Find the initial speed
Answer to Problem 13.149P
The initial speed
Explanation of Solution
Given information:
The weight of the bullet B
The weight of the block A
The weight of the block C
The coefficient of friction between the blocks and plane
The distance between the upper block A and lower block A
The distance between the upper block C and lower block C
The acceleration due to gravity (g) is
Calculation:
Show the free body diagram of the block A as the bullet passes through it as Figure (1).
The expression for the principle of conservation of momentum to the bullet and block A as follows;
Here,
Since the block A is at rest initially, so the velocity
Substitute 0 for
Calculate the mass of the bullet
Substitute
Calculate the mass of the block A
Substitute
The expression for the normal force acting on the block A as follows;
The expression for the work done
Substitute
The expression for the initial kinetic energy of the block A
The final kinetic energy of the block A
The expression for the principle of work-energy to the block A after the bullet just passes through it as follows;
Substitute
Substitute 0.25 for
Show the free body diagram of the block C as the bullet passes through it as in Figure (2).
The expression for the principle of conservation of momentum to the bullet and block A as follows;
Here,
The initial velocity of the block C
Substitute 0 for
Calculate the mass of the block C
Substitute
The expression for the normal force acting on the block C as follows:
The expression for the work done
The expression for the initial kinetic energy of the block C
The final kinetic energy of the block C with bullet embedded
The expression for the principle of work-energy to the block C after the bullet just gets embedded in the block as follows:
Substitute
Substitute 0.25 for
Substitute
Calculate the initial speed of the bullet
Consider the equation (1).
Substitute
Therefore, the initial speed
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Chapter 13 Solutions
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