# Impulse Momentum Exam 1 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=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.
Initial and final momentum vectors of ball are shown in the figure below.
**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.
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**