C
1 answer:
Answer:
27J
3528J
Explanation:
First problem:
Given parameters:
Mass of tennis ball = 0.06kg
Velocity of tennis ball = 30m/s
Unknown:
Kinetic energy = ?
Solution:
Kinetic energy is the energy due to the motion of a body.
It is expressed as:
K.E = m v²
K.E = x 0.06 x 30² = 27J
Second problem:
Given parameters:
Mass = 30kg
Height = 12m
Unknown:
Potential energy = ?
Solution:
Potential energy is the energy due to the position of a body.
Mathematically;
Potential energy = mgh
m is the mass
g is the acceleration due to gravity
h is the height
Now;
Potential energy = 30 x 9.8 x 12 = 3528J
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(a) 0.165 m/s
The total initial momentum of the astronaut+capsule system is zero (assuming they are both at rest, if we use the reference frame of the capsule):
The final total momentum is instead:
where
is the mass of the astronaut
is the velocity of the astronaut
is the mass of the capsule
is the velocity of the capsule
Since the total momentum must be conserved, we have
so
Solving the equation for , we find
(negative direction means opposite to the astronaut)
So, the change in speed of the capsule is 0.165 m/s.
(b) 520.8 N
We can calculate the average force exerted by the capsule on the man by using the impulse theorem, which states that the product between the average force and the time of the collision is equal to the change in momentum of the astronaut:
The change in momentum of the astronaut is
And the duration of the push is
So re-arranging the equation we find the average force exerted by the capsule on the astronaut:
And according to Newton's third law, the astronaut exerts an equal and opposite force on the capsule.
(c) 25.9 J, 390.6 J
The kinetic energy of an object is given by:
where
m is the mass
v is the speed
For the astronaut, m = 125 kg and v = 2.50 m/s, so its kinetic energy is
For the capsule, m = 1900 kg and v = 0.165 m/s, so its kinetic energy is