Mechanics question plz help

plz help me with the following questions if u can

a gun of mass 5000kg discharges a shot of mass 25kg. The gun recoils against a constant force of 10kN which brings it to rest in 1.25s. Find the speed of the shot.

The answer is 500 ms^-1

a shell is travelling horizontally at 400ms^-1 when it explodes into two pieces whose masses are in the ratio 2:3. The larger piece has a speed of 800ms^-1 in the origional direction of motion. given that the smaller piece also moves horizontally after the explosion find its velocity.

the answer is 200ms^-1 in the opposite direction

thanx

Reply 1

idiopathic

charna

plz help me with the following questions if u can

a gun of mass 5000kg discharges a shot of mass 25kg. The gun recoils against a constant force of 10kN which brings it to rest in 1.25s. Find the speed of the shot.

See attachment.

Deceleration of Va
F = ma
a = F/m
a = -10000/4975
a = -2.01 ms^-2

Consider motion of Va horizontally:
let u=-Va
v = 0
a = -2.05 ms^-2
t=1.25s

so v=u+at
0 = -Va + -2.01*1.25
Va = -2.51m/s

Momentum before = momentum after
0 = -2.51*4975 + 25*Vs
Vs = (2.51*4975)/25
Vs= 500m/s

momentum1.JPG5.9KB

Reply 2

Christophicus

a shell is travelling horizontally at 400ms^-1 when it explodes into two pieces whose masses are in the ratio 2:3. The larger piece has a speed of 800ms^-1 in the origional direction of motion. given that the smaller piece also moves horizontally after the explosion find its velocity.

the answer is 200ms^-1 in the opposite direction

m = 2m/5, u = 400ms^-1, v = v
m = 3m/5, u = 400ms^-1, v = 800ms^-1

Conservation of momentum
800m/5 + 1200m/5 = 2mv/5 + 2400m/5
400 = 0.4v + 480
400 - 480 = 0.4v
v = (400 - 480)/0.4 = -80/0.4 = -200ms^-1

Sign has changed, therefore direction of motion has changed, therefore speed of the smaller piece is 200ms^-1 in the opposite direction.

Reply 3

idiopathic

Widowmaker

a gun of mass 5000kg discharges a shot of mass 25kg. The gun recoils against a constant force of 10kN which brings it to rest in 1.25s. Find the speed of the shot.

The answer is 500 ms^-1

F = ma
-10000 = 25a
a = -400ms^-2

u = ?, v = 0, a = -400, t = 1.25
u = v - at
u = 0 - (-400)(1.25)
u = 500ms^-1

I'm not sure about the working - the shot (25kg) is not decelerating.