A gymnast falls from the high bar and lands on a 10 cm thick gymnastics mat. The

Question

A gymnast falls from the high bar and lands on a 10 cm thick gymnastics mat. The gymnast strikes the back of his head against the mat during his landing. His head is moving at 7 m/s when it first strikes the mat. The mass of his head is 5 kg. The impact ends when the gymnast’s head comes to a stop after deflecting the mat 6.5 cm.

How much kinetic energy does the gymnast’s head have at the instant just before it contacts the mat?

How much work does the mat do to stop the motion of the gymnast’s head?

What average impact force does the mat exert on the gymnast’s head during the impact?

Estimate the peak impact force exerted by the mat on the gymnast’s head.

Estimate the peak acceleration of the gymnast’s head.

Express this peak acceleration in g’s.

Explanation / Answer

A)

kinetic energy does the gymnast’s head have at the instant just before it contacts the mat is 1/ 2 mv2

KE = 1/ 2 mv2 = 1/2 X 5 X 7X 7

KE=1/2 X 245

KE= 122.5 J

B)

the impact force is F = m g rinitial / rfinal

F = 5X9.8X 0.1 / 0.065

F = 4.9 / 0.065

F = 75.38N

C)

peak impact force Fpeak = P2 / 2m

Fpeak = (mv)2 / 2m

= (5 X 7)2 / 2 X5

= 35/10

Fpeak =3.5N

D)

peak accelaration Fpeak = m apeak

apeak = Fpeak / m

= 3.5 / 5

apeak = 0.7 m/s2

E)

accelaration in grams is 70 cm/s2

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.