Question

Boxing gloves are padded to lessen the force of a blow.

(a) Calculate the force exerted by a boxing glove on an opponent's face, if the glove and face compress 7.00 cm during a blow in which the 8.00 kg arm and glove are brought to rest from an initial speed of 10.0 m/s.
N
(b) Calculate the force exerted by an identical blow in the gory old days when no gloves were used and the knuckles and face would compress only 2.00 cm. (Assume the total mass of the arm remains 8.00 kg.)
N
(c) Discuss the magnitude of the force with glove on. Does it seem high enough to cause damage even though it is lower than the force with no glove?

In a downhill ski race surprisingly little advantage is gained by getting a running start. This is because the initial kinetic energy is small compared with the gain in gravitational potential energy even on small hills. To demonstrate this, find the final speed and the time taken for a skier who skies 70.0 m along a 25° slope neglecting friction for the following two cases. (Note that this time difference can be very significant in competitive events so it is still worthwhile to get a running start.)

(a) starting from rest
final speed
m/s
time taken
s

(b) starting with an initial speed of 3.00 m/s
final speed
m/s
time taken
s

(a) How high a hill can a car coast up (engine disengaged) if friction is negligible and its initial speed is 76.0 km/h?
m
(b) If, in actuality, a 750 kg car with an initial speed of 76.0 km/h is observed to coast up a hill to a height 11.0 m above its starting point, how much thermal energy was generated by friction?
J
(c) What is the average force of friction if the hill has a slope 2.5° above the horizontal? (Explicitly show on paper how you follow the steps in the Problem-Solving Strategy for energy found on pages 159 and 160. Your instructor may ask you to turn in this work.)
N (down the slope)

Answer 1

Boxing gloves

a)here v² = u² + 2as

and v=0 so 0 = (10)² + 2*a*(.07)

=> a = 100/.14 = 714.28 m/s²

=> F = ma = 8*714.28 = 5714.24 N

b)

=> 0 = (10)² + 2*a*(.02)

=> a = 100/.04 = 2500 m/s²

=> F = ma = 8*2500 = 10000 N

c) here it clear that the force on the face with no gloves is higher to with gloves.

In a downhill ski race surprisingly

a)From Rest position:
Potential Enegy = Kinetic Energy
=> m*g*h*sin(25) = 1/ 2 m *V²

cancel out m
=> 9.8 * 70 * 0.423 = 0.5 V² => V = 24.1 m/s

we know that

v = u + at

here a = g*sin(25) = 9.8*.423 = 4.145 m/s²

24.1 = 0 + 4.145*t

t = 24.1/4.145 = 5.81sec

b)
With Initial velocity of 3.0m/s:
Change in Kinetic energy = Change in Potential Energy
1/2*m*V₂² - 1/2 *m*V₁² = mgh*sin(25)
1/2*m*V₂² - 1/2*m*(3)² = m*9.8*70*0.423

Cancel out the m
0.5 *V₂² = 290.18 - 4.5 = 285.68

V₂ = sqrt(571.36)
V₂ = 23.9 m/s

v = u + at

=> V₂ = V₁ + at

=> 23.9 = 3 + 4.145t

=> t = 20.9/ 4.145 = 5.04sec

a)

v = 76km/h = (76*1000)/(60*60) = 21.11 m/s

kinetic energy = potential energy

=> 1/2*m*v² = mgh

=> h = 0.5*(21.11)² / (9.8) = 22.74m

b) thermal energy was generated by friction = KE - PE

KE = 0.5*750*(21.11)² = 167111.25 J

PE = 750*9.8*11 = 80850 J

thermal energy = 167111.25 - 80850 = 86261.25 J