Unit-1 Solutions 1.7 Impulse & Linear Momentum page - 88 Impulse... · 1.7 Impulse & Linear Momentum page - 88 ... 11th grade Fizx Unit-1 Force & Motion 1.7 Impulse & Linear Momentum

11th grade Fizx

Unit-1 Force & Motion

1.7 Impulse & Linear Momentumpage - 88

Solutions

Problems

Force & Motion Chapter-1

88

1. A 2 kg ball moves toward a wall and bounces back as shown in the figures.

Calculate the average force applied by the wall on the ball interacts with the wall for 0,02 s. (Ignore the rotational motion of the ball.) 2. A ball of mass 2 kg strikes the ground and bounces as shown in the figure.

Calculate the impulse imparted by the ground on the ball.

3. Force-time graph of an object of mass 0,5 kg that is at rest over a horizontal surface is given.

What is the velocity of the object at t=4 s? 4. A skating grandmother of mass 80 kg moving with 6 m/s holds her 40 kg grand child that is stationary over a frictionless horizontal surface.

What is the final velocity of the combined mass (vfinal)?

F→

net .Δt = m.Δ v→

F→

net .Δt = m.(v→

final− v→

initial )

F→

wall .0,02 = 2.(-8 - 10)

F→

wall = -1800 N

+

11th grade Fizx



Solutions

Problems


88







P→

final−P→

initial ΔP→

37 !37 !

Impulse=F→

net .Δt = ΔP→

Impulse=F→

net .Δt = P→

final− P→

initial

Impulse= 2.m.v.sin37 !

Impulse= 2.2.10.0,6

Impulse= 24 kg.m / s

11th grade Fizx



Solutions

Problems


88







The area of F - t graph gives the change in momentum.

ΔP1 =5.12

= 2,5 kg.m / s

ΔP2 = 5.1 = 5 kg.m / s

ΔP3 =5.12

= 2,5 kg.m / s

ΔP4 = −5.12

= −2,5 kg.m / s

⎫

⎬

⎪⎪⎪⎪

⎭

⎪⎪⎪⎪

⇒

ΔPtotal = 7,5 kg.m / s

7,5 =0,5.v final ⇒ v final = 15 m / s

11th grade Fizx



Solutions

Problems


88







ΣP→

initial = ΣP→

final

(80.6)=(80+40).v

v = 4 m / s

+

11th grade Fizx



Solutions

Chapter-1 Force & Motion

89

5. A wooden block of mass 990 g is stationary over a frictionless horizontal surface. A bullet of mass 10 g moving with a speed of 400 m/s embeds the wooden block.

What is the speed of the combined mass? 6. An explosion blows a rock into three pieces. Two pieces fly off at right angles to one another. 1 kg piece moves with 12 m/s and 2 kg piece moves with 8 m/s. What is the mass of the third piece if it has a speed of 50 m/s after explosion?

7. The path followed by the box with respect to the truck is given in the figure.

What will be the velocity of the truck after the box falls on the truck? 8. A box of mass “m” is thrown from a truck of mass “4m” with respect to the truck as shown in the figure.

What is the final velocity of the truck? (Ignore friction.)

ΣP→

initial = ΣP→

final

(0,01.400)=(0, 99+0,01).v

v = 4 m / s

+

11th grade Fizx



Solutions


89






P→

1

P→

3

P→

2

after explosionbefore explosion

P→

initial = 012 kg.m / s

16 kg.m / s

P3 = 20 kg.m / s

P3 = m3 .v3

20=m3 .50

m3 = 0,4 kg

11th grade Fizx



Solutions


89






+

vbox(wrt the ground)= 10 m / s

ΣP→

initial = ΣP→

final

(m.10)+(4m.10)=(m+4m).v

v = 10 m / s

11th grade Fizx



Solutions


89






+

vbox(wrt the ground)= 2 m / s

ΣP→

initial = ΣP→

final

(5m.10)=(m.2)(4m.v)

v = 12 m / s

11th grade Fizx



Solutions


9. Two billiard balls (13 & 5) move toward each other over a frictionless horizontal surface as shown in the figure. Balls make an elastic head-on collision.

What are the velocities of the balls after the collision? (Ignore the rotational motion of the balls.) 10. Two objects of masses “mA” and “mB” move at speeds of 8 m/s and 4 m/s over a frictionless horizontal surface. After the objects make elastic head-on collision, the object of mass mA moves at a speed of 2 m/s.

Calculate the ratio of the masses (mA/mB) of the objects.

11. Two objects K and L move on a frictionless path. They collide at point P. In Figure-1 and Figure-2, the positions and directions of motions of the objects are given for the same time intervals before and after the collision.

What is the ratio of the masses (mK/mL) of the objects? 12. The objects X and Y are thrown on the frictionless horizontal surface at the same time with initial speeds of v1 and v2 respectively and they collide at point M after 2 seconds.

If the objects X and Y are at the points K and N respectively 4 seconds after collision, calculate the ratio of their masses (mx/my).

90

+

ΣP→

initial = ΣP→

final

(3.4)+(2.(-6))=(3.u1)+(2.u2 )

3.u1 = −2.u2 ⇒u1 =−2.u2

3

v→

1+u→

1 = v→

2+u→

2

4+u1 = -6+u2 ⇒u1 - u2 = -10

−2.u2

3- u2 = -10 ⇒u2 = 6 m / s

u1 = -4 m / s

11th grade Fizx



Solutions








90

+

v→

A+u→

A = v→

B+u→

B

8+2 = -4+uB ⇒uB = 14 m / s

ΣP→

initial = ΣP→

final

(mA.8)+(mB.(-4))=(mA.2)+(mB.14)(mA.8)-(mA.2)=(mB.14)+(mB.4)6mA = 18mB

mA

mB= 3

11th grade Fizx



Solutions








90

+

Collision takes place at point P;Initial velocities are

v→

K =3v and v→

L =-vfinal velocities are

v→

K =-v and v→

L = 2v

ΣP→

initial = ΣP→

final

(mK.3v)+(mL.(-v))=(mA.(-v))+(mL.2v)(3mK )+(mK )=(2mL )+(mL )mK

mL

= 34

11th grade Fizx



Solutions








90

+

Collision takes place at point M;Initial velocities are

v→

X = 2v and v→

Y =-4vfinal velocities are

v→

X =-v and v→

Y = v / 2

ΣP→

initial = ΣP→

final

(mX .2v)+(mY.(-4v))=(mX .(-v))+(mY.(v / 2))

3mX =92

mY

mX

mY

= 32

11th grade Fizx



Solutions


91

13. Two objects with masses m and 3m are released from the points K and P at the same time. They move through the friction-free path. They collide and stick to each other at point O.

What will be the maximum height reached by the combined mass in terms of “h”? 14. Three objects of masses mx, my and mz are moving on a frictionless horizontal surface. The objects collide at point O and stick to each other. The combined mass moves along the direction-5. The mass of X and Y are given as m and 3m, respectively.

a) What is the mass of the object Z in terms of

“m”? b) If only objects Y and Z collide and stick at

point O, in which direction would they go?

15. Two balls A and B are moving at constant speeds of “vA“ and “vB”. The masses of the objects are “2m” and “3m” respectively. They collide at point O and move together as a single object in the direction-I as shown in the figure.

What is the ratio of the speeds of the objects (vA/vB)? 16. The object of mass “m” moves in a frictionless horizontal plane with the velocity “v”. Then it collides objects of masses “2m” and “3m” which are initially stationary. After collision object of mass “m” stops and the velocities of the objects having masses of “2m” and “3m” are v1 and v2.

Calculate the ratio of the velocities v1 and v2.

PE=0

For mass m;

mg4h= 12

mv 12 ⇒ v 1

2 = 8gh

For mass 3m;

3mg4h= 12

3mv 22 ⇒ v 2

2 = 8gh

⎫

⎬

⎪⎪⎪

⎭

⎪⎪⎪

⇒ v 1 = v 2 = v

+

ΣP→

initial = ΣP→

final

(m.v)+(3m.(-v))=(m+4m).v / ⇒ v / = -v2

For combined mass ;

4mgh/= 124m v/( )2

gh/ = 8gh⇒h/ = h

11th grade Fizx



Solutions


91









a)Pfx

= 3P =3m.v ⇒mv = P

Pfy= P =mz.v -mv ⇒mz = 2m

b)Pix

= 3m.v

Piy= 2m.v

⎫⎬⎪

⎭⎪⇒ combined mass move in direction - 4

11th grade Fizx



Solutions


91









Pix= 2m.vA

Pfx= P2

⎫⎬⎪

⎭⎪⇒ 2m.vA = P

2

Pix= 3m.vB

Pfy= 3P

2

⎫⎬⎪

⎭⎪⇒ 3m.vB = 3P

2

vA

vB

= 32

11th grade Fizx



Solutions


91









ΣP→

initial = ΣP→

final

ΣP→

initialx = ΣP→

final x

mv= 2m.v1 .0,8( )+ 3m.v2 .0,6( )8v1 + 9v2 = 5

ΣP→

initialy = ΣP→

final y

0= 2m.v1 .0,6( )− 3m.v2 .0,8( )v 1 = 2v 2

⎫

⎬

⎪⎪⎪⎪⎪⎪⎪

⎭

⎪⎪⎪⎪⎪⎪⎪

⇒

v 1 = 0,4 m / s

v 2 = 0,2 m / s

+

+

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Unit-1 Solutions 1.7 Impulse & Linear Momentum page - 88 Impulse... · 1.7 Impulse & Linear Momentum page - 88 ... 11th grade Fizx Unit-1 Force & Motion 1.7 Impulse & Linear Momentum