Impulse and momentum?

Question

In these questions, take the zero of potential energy at the ground level shown.

1. Dylan tees off at the first hole of a golf course. The 0.050kg ball takes off with a speed of 70m/s^-1. The golf club is in contact with the ball for 1milisecond(1x10^-3 seconds). Find:

a) the change in momentum of the golf ball:

b) the impulse of the force exerted by the club

c) the average force excerted by the club:

2. Superman is flying up to catch Lois Lane(50kg) who is falling at 15m/s^-1 when he catches her. Their final velocity is upwards at 10m/s^-1.

a) what change in velocity does Lois experience?

b) what is her change in momentum?

c)It takes 0.1s for superman to catch lois. Find the average force which he exerts on her:

d)what advice would you give superman about catching lois next time?

3. What average force is necessary to stop a hammer with 25Ns momentum in 0.05s?

a) how does the direction of the force compare to the hammer's path?

4. Two disks on a frictionless surface were initially at rest. They were driven apart by an explosion with velocities 5cm/s^-1 and 2cm/s^-1. What is the ratio of their masses?

 

Answer 1

1)

Mass of the ball, m =0.05 kg

Speed of the ball,Δv = 70 m/s

Time taken, Δt = 1 ms=0.001s

a)

Calculate change in momentum

ΔM =mΔv

Substitute 0.05 kg for m and 70 m/s for Δv in above relation

ΔM=0.05*70=3.5 kg-m/s

b)

Calculate the impulse of the force exerted by the club by the impulse momentum

FΔt=ΔM

Substitute 3.5 kg-m/s for DM

FΔt=3.5 kg-m/s=3.5 N-s

c)

Calculate average force by using

FΔt=ΔM

F=ΔM/Δt

Substitute 3.5 kg-m/s for ΔM and 0.001s for Δt

F=3.5/0.001=3500 N

 

Answer 2

2)

a)

Calculate change in velocity by using

Δv =v-u

Here u is the initial velocity and v is the final velocity.

Substitute -15 m/s for u and 10 m/s for v in above relation.

Δv =10-(-15)=25 m/s

b)

Calculate change in momentum

ΔM =m|Δv|

Substitute 50 kg for m and 25 m/s for Dv in above relation

ΔM=50*25=1250 kg-m/s

c)

Calculate average force by using

FΔt=ΔM

F=ΔM/Δt

Substitute 1250 kg-m/s for ΔM and 0.1s for Δt

F=1250/0.1=12500 N

3)

Calculate average force

FΔt=ΔM

F=ΔM/Δt

Substitute 25 Ns for ΔM and 0.05s for Δt

F=25/0.05=500 N

 

4)

u1=u2=0
v1=5 cm/s
v2=2 cm/s

Using conservation of momentum
m1u1+m2u2=m1v1+m2v2
0=m1*5+m2*2
m1/m2=-2/5
m1/m2=2/5 [negative sign is discarded because mass cannot be negative]