Impulse Momentum Exam1 and  Problem Solutions
 
1. An object travels with a velocity 4m/s to the east. Then, its direction of motion and magnitude of velocity are changed. Picture given below shows the directions and magnitudes of velocities. Find the impulse given to this object.
 
 
impulse_1
 
 
 
 
 
 
 
I=F.Δt=Δp=m.ΔV
where ΔV=V2-V1=-3-4=-7m/s
I=m.ΔV=3.(-7)=-21kg.m/s
 
2. Ball having mass 4kg and velocity 8m/s travels to the east. Impulse given at point O, makes it change direction to north with velocity 6m/s. Find the given impulse and change in the momentum.
impulse_2
 
 
 
 
 
 
 
 
 
 
 
Initial and final momentum vectors of ball are shown in the figure below.
impulse_2solution
 
 
 
 
 
 
 
 
 
P1=m.V1=4kg.8m/s=32kg.m/s
P2=m.V2=4kg.6m/s=24kg.m/s
ΔP=P2+P1 (vector addition)
ΔP2=P22+P12=m2(v22+v12)
ΔP2=16.100
ΔP=40kg.m/s
Impulse=change in momentum
I=ΔP=40kg.m/s
 
3. Find the impulse and force which make 12m/s change in the velocity of object having 16kg mass in 4 s.
F.Δt=ΔP=m.ΔV
F.4s=16kg.12m/s
F=48N
F.Δt=Impulse=192kg.m/s
 
4. Applied force vs. time graph of object is given below. Find the impulse of the object between 0-10s.
 
impulse_3
 
 
 
 
 
 
 
 
 
 
 
 
 
Area under the force vs. time graph gives us impulse.
F.Δt=20.2/2+20.(6-2)+20.(10-6)/2
F.Δt=140kg.m/s

5. A ball having mass 500g hits wall with a10m/s velocity. Wall applies 4000 N force to the ball and it turns back with 8m/s velocity. Find the time of ball-wall contact.
 
F.Δt=ΔP=m.ΔV=m.(V2-V1)
-4000.Δt=0,5kg.(8-10)
Δt=0,00025s
 
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