WORK and ENERGY?

Question

1) A baseball (m=140g) travelling 35m/s moves a fielder's glove backward 25cm when the ball is caught. What was the average force exerted by the ball on the glove?

2) Snoopy throws a basketball through a hoop. The ball left his paws at a height of 0.5m with a speed of 9m/s. Calculate its speed when it swished through the hoop. The hoop is at a height of 3m and it is 5m along the court from Snoopy.

Answer 1

Snoopy is a cartoon character, and the laws of physics don't apply in cartoons.

Answer 2

1) p=mv , p=∆f/∆t ==> mv=∆f/∆t ==> ∆f=mv∆t

     v=∆x/∆t

     ∆t=35/(25x10^-2)

     ∆f=(140x10^-3)x35x(35/(25x10^-2))=686N

2)E1=E2 (g=10)

   mg(h1)+1/2m(v1)^2=mg(h2)+1/2m(v2)^2

   g(h1)+1/2(v1)^2=g(h2)+1/2(v2)^2

   (10x0.5)+(0.5x81)=(10x3)+(0.5x(v2)^2 )

   ...

   v2=√31

Answer 3

<< A baseball (m=140g) travelling 35m/s moves a fielder's glove backward 25cm when the ball is caught. What was the average force exerted by the ball on the glove? >>

Use conservation of energy for this problem.

Kinetic energy of ball = energy absorbed by glove

(1/2)(m)V^2 = Fd

where

m = mass of baseball = 140 g = 0.140 kg.

V = velocity of baseball = 35 m/sec.

d = distance that glove moved when ball was caught = 25 cm = 0.25 m.

F = force exerted by ball on glove

Substituting appropriate values,

(1/2)(0.14)(35^2) = F(0.25)

Solving for "F",

F = 343 Newtons

<< Snoopy throws a basketball through a hoop. The ball left his paws at a height of 0.5m with a speed of 9m/s. Calculate its speed when it swished through the hoop. The hoop is at a height of 3m and it is 5m along the court from Snoopy.>>

Let

A = the angle at which Snoopy throws the basketball

tan A = (3 - 0.5)/5 = 2.5/5

tan A = 0.5

A = arc tan 0.5

A = 26.57

Determine the maximum height at which the basketball will reach given the initial speed and the angle of launching.

The maximum height is calculated as follows:

Vf^2 - Vo(sin 26.57)^2 = 2(gh)

where

Vf =  velocity of the basketball at its peak = 0

Vo = initial speed of the basketball = 9 m/sec. (given)

g = acceleration due to gravity = 9.8 m/sec^2 (constant)

h = maximum height that the ball will attain

Substituting appropriate values,

0 - (9 * sin 26.57)^2 = 2(-9.8)(h)

NOTE the negative sign attached to the acceleration due to gravity. This denotes that the basketball slows down as it is going up.

Solving for "h",

h = 0.83 meter

The maximum height that the basketball will attain (as measured from the ground) is 0.5 + 0.83 = 1.33 m.

Since the hoop is 3 meters above Snoopy, then Snoopy will completely miss the basket. He will throw an air-ball at these conditions!!!

Answer 4

classic conservation of momentum problems

baseball mass 140grams = .14 kg

.14 kg x 35 m/s = .25 m x  force

4.9 newtons = .25 ( newtons)

average force  =19.6 newtons

2) final velocity = initial velocity + change in velocity

the ball moves upward 2.5 meters (3-.5) against the force of gravity

D= .5 aT^2 ; 2.5 = .5 (9..8)T^2;   T^2= .51  ;  T = .714 seconds

V=at = 9.8 x .714 seconds = 7 m/s

9 m/s initial velocity - 7m/s change = 2 m/s final velocity.

I did some rounding so you may wish to run the numbers yourself