Answer: m = 0.035kg = 35g
Explanation: Momentum p=0.140kgm/s
Velocity v=4m/s
Mass m=?
Formula-
Momentum depends on the mass of the object in motion and its velocity.
The equation for momentum is
p = mv
m = p/v
m = 0.140/4
m = 0.035kg
m = 35g
Hence, in the toy dart gun mass of the dart is 0.035kg.
Answer:
Δω = -5.4 rad/s
αav = -3.6 rad/s²
Explanation:
<u>Given</u>:
Initial angular velocity = ωi = 2.70 rad/s
Final angular velocity = ωf = -2.70 rad/s (negative sign is
due to the movement in opposite direction)
Change in time period = Δt = 1.50 s
<u>Required</u>:
Change in angular velocity = Δω = ?
Average angular acceleration = αav = ?
<u>Solution</u>:
<u>Angular velocity (Δω):</u>
Δω = ωf - ωi
Δω = -2.70 - 2.70
Δω = -5.4 rad/s.
<u> Average angular acceleration (αav):</u>
αav = Δω/Δt
αav = -5.4/1.50
αav = -3.6 rad/s²
Since, the angular velocity is decreasing from 2.70 rad/s (in counter clockwise direction) to rest and then to -2.70 rad/s (in clockwise direction) so, the change in angular velocity is negative.
Answer:
final temperature will be 0 degree C
Total amount of ice will be

total amount of water

Explanation:
After thermal equilibrium is achieved we can say that
Heat given by water = heat absorbed by ice cubes
so we will have
Heat given by water to reach 0 degree C



heat absorbed by ice cubes to reach 0 degree



so we will have

so here we can say that few amount of water will freeze here to balance the heat



so final temperature will be 0 degree C
Total amount of ice will be


total amount of water


<span>So we want to know what happens to the momentum of the ball that rolls down hill and hits a box. So we need to use the law of conservation of momentum which states that the momentum must be conserved. It cant be transformed into inertia or mass. It can only be transferred to other object via some interactions like collisions. So it has to be a. transferred to the box and that is the correct answer. </span>