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## Impulse Momentum Exam1 and Problem Solutions

**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.

**I=F.Δt=Δp=m.ΔV**

** where ΔV=V _{2}-V_{1}=-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.

Initial and final momentum vectors of ball are shown in the figure below.

**P _{1}=m.V_{1}=4kg.8m/s=32kg.m/s**

** P _{2}=m.V_{2}=4kg.6m/s=24kg.m/s **

**ΔP=P _{2}+P_{1} (vector addition)**

** ΔP ^{2}=P_{2}^{2}+P_{1}^{2}=m^{2}(v_{2}^{2}+v_{1}^{2}) **

**ΔP _{2}=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.

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.(V _{2}-V_{1}) **

**-4000.Δt=0,5kg.(8-10)**

** Δt=0,00025s**

Author: Mrs. Şerife (Erden) SARICA

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