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.
The acceleration of the air plane is 
<u>Explanation:</u>
Given:
The mass of the air plane = 1492.3 kg
Force of each four engine = 1447.5 N
So, the total force of four engines can be calculated as = 4(1447.5) = 5790 N
The force that acts on the object is equal to the product of mass (m) and its acceleration. It can express by the below formula,

The above equation can be written as below to find acceleration,

Now. Substitute the given values, we get,

The force needed is 5250N
Answer:
a)11.25 J
b)Number of revolution = 1
Explanation:
Given that
Radius ,r= 0.8 m
m= 0.3 kg
Initial speed ,u= 10 m/s
final speed ,v= 5 m/s
a)
Initial energy


KEi= 15 J
Final kinetic energy


KEf=3.75 J
The energy transformed from mechanical to internal = 15 - 3.75 J = 11.25 J
b)
The minimum value to complete the circular arc

Now by putting the values

V= 2.82 m/s
So kinetic energy KE


KE=1.19 J
ΔKE= KEi - KE
ΔKE= 15- 1.19 J
ΔKE=13.80 J
The minimum energy required to complete 2 revolutions = 2 x 11.25 J
= 22.5 J
Here 22.5 J is greater than 13.8 J.So the particle will complete only one revolution.
Number of revolution = 1
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