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Draw an appropriate graph of the data and, from
Chapter 9, Problem 43P(choose chapter or problem)
Problem 43P
Draw an appropriate graph of the data and, from the slope of the best-fit line, determine the impulse.
a. A bullet of mass m is fired into a block of mass M that is at rest. The block, with the bullet embedded, slides distance d across a horizontal surface. The coefficient of kinetic friction is μk. Find an expression for the bullet’s speed vbullet.
b. What is the speed of a 10 g bullet that, when fired into a 10 kg stationary wood block, causes the block to slide 5.0 cm across a wood table?
Questions & Answers
QUESTION:
Problem 43P
Draw an appropriate graph of the data and, from the slope of the best-fit line, determine the impulse.
a. A bullet of mass m is fired into a block of mass M that is at rest. The block, with the bullet embedded, slides distance d across a horizontal surface. The coefficient of kinetic friction is μk. Find an expression for the bullet’s speed vbullet.
b. What is the speed of a 10 g bullet that, when fired into a 10 kg stationary wood block, causes the block to slide 5.0 cm across a wood table?
ANSWER:
Step 1 of 3
a) We need to find an expression for the bullet's speed.
By applying the conservation of momentum we can write
\(m v_{b u l l e t}+M v_{b}=(m+M) v_{f x}\)
The initial velocity of the block, \(v_{b}=0\)
So,
\(m v_{\text {bullet }}=(m+M) v_{f x}\)
Implies,
\(v_{b u l l e t}=\frac{(m+M) v_{f x}}{m} \ldots \ldots \ldots \ldots(1)\)
Using the kinematics equation,
\(v_{1 x}^{2}=v_{0 x}^{2}+2 a d\)
\(v_{1 x}^{2}=v_{f x}^{2}+2 a d\)
That is,
\(v_{f x}=\sqrt{-2 a d}\)