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Your forehead can withstand a force of about 6.0 kN before
Chapter 7, Problem 28P(choose chapter or problem)
Your forehead can withstand a force of about 6.0 kN before fracturing, while your cheekbone can withstand only about 1.3 kN. Suppose a 140 g baseball traveling at 30 m/s strikes your head and stops in 1.5 ms.
a. What is the magnitude of the force that stops the baseball?
b. What force does the baseball exert on your head? Explain.
c. Are you in danger of a fracture if the ball hits you in the forehead? On the cheek?
Questions & Answers
QUESTION:
Your forehead can withstand a force of about 6.0 kN before fracturing, while your cheekbone can withstand only about 1.3 kN. Suppose a 140 g baseball traveling at 30 m/s strikes your head and stops in 1.5 ms.
a. What is the magnitude of the force that stops the baseball?
b. What force does the baseball exert on your head? Explain.
c. Are you in danger of a fracture if the ball hits you in the forehead? On the cheek?
ANSWER:Step 1 of 3
a)
Here we have to calculate the force by which the ball stopped.,
The mass of the ball is,
\(m_{\text {ball }}=140 \mathrm{~g}=0.14 \mathrm{~kg}\).
.
The initial speed of the ball was,
\(v_{i}=30 \mathrm{~m} / \mathrm{s}\).
The final velocity is,
\(v_{f}=0\).
The time taken to stop is,
\(\Delta t=1.3 \mathrm{~ms}\).
The acceleration is,
\(a=\frac{v_{f}-v_{i}}{\Delta t}\)
\(=\frac{-30}{0.0015 \mathrm{~s}}=20000 \mathrm{~m} / \mathrm{s}^{2}\).
The force required to stop is,
\(F=m_{\text {ball }} a=0.14 \times 20000=2800 \mathrm{~N}\).
The magnitude of the force that stops the ball is 2800 N.