Answer:
a)40.77N
b)0.11seg
Explanation:
The bullet has a kinetic energy:
[tex]K=1/2*m*v^{2} = 1/2*0.0078kg*575m/s=2.2425J[/tex]
When the bullet stops this energy goes to zero, as the energy must be conserved the work done by the head of the superhero must be equal to the original energy of the bullet:
[tex]W=K[/tex]
Considering an average constant force, the work can be calculated as:
[tex]W=F*d=K[/tex]
Solving for F:
[tex]F=K/d=2.2425J/0.055m=40.77N[/tex]
The acceleration(on the opposite direction of motion) on the bullet will be:
[tex]a=F/m=40.77N/0.0078kg=5226.9 m/s^{2}[/tex]
The velocity of the bullet considering a constant acceleration can be calculate as:
[tex]V=V_{0} - a*t[/tex]
It stops moving when V=0 so:
[tex]V_{0} - a*t=0=>t=V_{0}/a=\frac{575m/s}{5226.9m/s^{2} } =0.11seg[/tex]
Answer:
a) 23444.3 N
b) 0.191 ms
Explanation:
Given:
Mass of the bullet m = 7.8 g = 7.8 * 10⁻³ Kg
Initial speed u = 575 m/s
Final speed v = 0
Distance covered s = 5.50 cm = 0.055 m
(a)
According to work energy theorem
Work done W = Change in Kinetic energy
hence, force*distance = 1/2*mass*velocity²
that is, F*S = (1/2)mu²
F*0.055 = 0.5 * 7.8 * 10⁻³ * (575)^2
F = 23444.3 N
(2)
From Impulse definition
force*time = change in momentum
where momentum = mass * velocity
F*t = Change in momentum = m* u
23444.3t = 7.8*10⁻³ * 575
Time, t = 0.191 ms
