CBSE PHYSICS: IX:Force and laws of motion solved Problems
1. An athlete runs a certain rest before taking a long jump. Why?
Solution: An athlete runs a certain distance to accelerate himself and gain enough momentum so that he can jump through the maximum possible length.
2. Springs are provided in car seats. Why?
Solution: The springs in the car seats absorb shock (sudden jumps) due to the roughness of the road. Thus, making the ride more comfortable.
3. A gun of mass 1500 kg fires a shell of mass 15kg with velocity 150 m/s. calculate velocity of recoil of the gun.
Solution: Before firing, total momentum of the gun and shell is = 0 (they were all at rest)
After firing, the momentum of the shell = 15 X 150 = 2250 Ns
The momentum of the gun is = 1500v Ns
By conservation of momentum,
Total momentum before firing = Total momentum after firing
0 = 2250 + 1500v
v = -2250/1500 = -1.5 m/s
4. Why cricketer pulls his hands backwards while catching the ball
6. What is impulse of Force?
I = F x t= change in p
Like force, impulse of force is also a vector quantity. Direction of impulse of force is same as the direction of force. Unit of impulse of force is kg m/s or Ns.Like force, impulse of force is also a vector quantity. Direction of impulse of force is same as the direction of force. Unit of impulse of force is kg m/s or Ns.
1. An athlete runs a certain rest before taking a long jump. Why?
Solution: An athlete runs a certain distance to accelerate himself and gain enough momentum so that he can jump through the maximum possible length.
2. Springs are provided in car seats. Why?
Solution: The springs in the car seats absorb shock (sudden jumps) due to the roughness of the road. Thus, making the ride more comfortable.
3. A gun of mass 1500 kg fires a shell of mass 15kg with velocity 150 m/s. calculate velocity of recoil of the gun.
Solution: Before firing, total momentum of the gun and shell is = 0 (they were all at rest)
After firing, the momentum of the shell = 15 X 150 = 2250 Ns
The momentum of the gun is = 1500v Ns
By conservation of momentum,
Total momentum before firing = Total momentum after firing
0 = 2250 + 1500v
v = -2250/1500 = -1.5 m/s
4. Why cricketer pulls his hands backwards while catching the ball
Solution: cricketer pulls his hands backwards while catching the ball. When he does so, momentum of the ball reduces slowly, and time t required for this increases. As per F =DP/t , as t increase, magnitude of F decreases. As a result cricketer can catch the ball, easily, without any injury.
5. Why A karate player in order to break a brick, hits it quickly
Solution: A karate player in order to break a brick, hitsit quickly, so in a short time there is a large change
in momentum and as per F =change in p/t as large force acts on the brick and it breaks.in momentum and as per F =change in p/t as large force acts on the brick and it breaks.in momentum and as per F =change in p/t as large force acts on the brick and it breaks.
Solution: A karate player in order to break a brick, hitsit quickly, so in a short time there is a large change
in momentum and as per F =change in p/t as large force acts on the brick and it breaks.in momentum and as per F =change in p/t as large force acts on the brick and it breaks.in momentum and as per F =change in p/t as large force acts on the brick and it breaks.
6. What is impulse of Force?
I = F x t= change in p
Like force, impulse of force is also a vector quantity. Direction of impulse of force is same as the direction of force. Unit of impulse of force is kg m/s or Ns.Like force, impulse of force is also a vector quantity. Direction of impulse of force is same as the direction of force. Unit of impulse of force is kg m/s or Ns.
7. A ball of 150 g is thrown at 20 m/s towards the batsman. He hits the ball in the direction oppsite to intial direction of motion with velocity 25 m/s. If the ball is hit in 0.01 s, calculate change in momentum of the ball and force applied by the batsman on the ball.
Solution: m = 150 g = 150/1000kg= 0.15 kg
u = 20 m/s, v = 25 m/s, t = 0.01 s
Initial momentum of the ball
pi = mu = (0.15)(20) = 3 kgm/s
Final momentum of the ball after being hit
pf = mv = (0.15)( - 25) = - 3.75 kgm/s
Here negative sign indicates that direction of motion of the ball after hitting is opposite to initial
direction of motion of the balls.
Change in momentum of the ball Dp = pf - pi = ( - 3.75 - 3) = - 6.75 kgm/s
So change in momentum of the bat = 6.75 kgm/s
Force applied by the bat,
F =Change in p/t= 6.75/ 0.01 = 675 kg m/s2 = 675 N
8.A bullet of 20 g is fired horizontally from a pistol of 2 kg mass with velocity 150 ms-1. How much would be the velocity of pistol in backward direction after firing the bullet ?
Solution : Mass of bullet m1 = 20 g = 0.02 kg
Mass of pistol m2 = 2 kg
Initial velocity of bullet u1 = 0 m/s
Initial velocity of pistol u2 = 0 m/s
Final velocity of the bullet = v1 = 150 ms-1
Final velocity of the pistol v2 = ?
According to law of conservation of momentum
m1v1 + m2v2 = m1u1 + m2u2
(0.02)(150) + (2)(v2) = (0.02)(0) + (2)(0)
v2 = - (0.02)(150)/2 = - 1.5 ms–1
Here, negative sign indicates that motions ofpistol and bullet are in opposite direction.
9. A bullet of mass 20 g is fired from a gun of mass 10kg with a velocity of 180m/s. Find the velocity of the recoil of the gun . Find the force required to stop the gun before it moves 20cm. Ans: Here we shall use the conservation of momentum to calculate the recoil velocity.
Momentum of the bullet + gun before firing = 0
Momentum of the bullet + gun after firing = (20 × 10 -3) (180) + (10)(v)
‘v’ is the recoil velocity of the gun.
So, by momentum conservation,
(20 × 10 -3 )(180) + (10)(u g ) = 0
=> u g = -0.36 m/s
The negative sign indicates that the gun’s velocity is directed opposite to the velocity of the bullet.
Now,
Distance travelled before coming to rest, S = 20 cm = 0.2 m
Let ‘a’ be the acceleration with which it stops.
Using, v 2 = u 2 + 2as
=> 0 = (180) 2 + 2a × 0.2
=> a = -8100 m/s 2
So, force on the bullet, F = ma = (20 × 10 -3 ) × (-8100) = -162 N
Negative sign indicates the force is against the motion of the bullet.
10. Two billiard balls each of mass 50 g moving in opposite directions with a speed of 10m/s colloid and rebound with the same velocity .What is the impulse imparted to each ball due to other?
Ans: Impulse = change is momentum.
Initial velocity of one billiard ball, u = 10m/s Final velocity after collision, v = -10m/s
Change in momentum in one billiard ball, Δ p = m(v-u) = -1kgm/s
Similarly, change in momentum of the other billiard ball, Δ p' = +0.1kgm/s
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Solution: m = 150 g = 150/1000kg= 0.15 kg
u = 20 m/s, v = 25 m/s, t = 0.01 s
Initial momentum of the ball
pi = mu = (0.15)(20) = 3 kgm/s
Final momentum of the ball after being hit
pf = mv = (0.15)( - 25) = - 3.75 kgm/s
Here negative sign indicates that direction of motion of the ball after hitting is opposite to initial
direction of motion of the balls.
Change in momentum of the ball Dp = pf - pi = ( - 3.75 - 3) = - 6.75 kgm/s
So change in momentum of the bat = 6.75 kgm/s
Force applied by the bat,
F =Change in p/t= 6.75/ 0.01 = 675 kg m/s2 = 675 N
8.A bullet of 20 g is fired horizontally from a pistol of 2 kg mass with velocity 150 ms-1. How much would be the velocity of pistol in backward direction after firing the bullet ?
Solution : Mass of bullet m1 = 20 g = 0.02 kg
Mass of pistol m2 = 2 kg
Initial velocity of bullet u1 = 0 m/s
Initial velocity of pistol u2 = 0 m/s
Final velocity of the bullet = v1 = 150 ms-1
Final velocity of the pistol v2 = ?
According to law of conservation of momentum
m1v1 + m2v2 = m1u1 + m2u2
(0.02)(150) + (2)(v2) = (0.02)(0) + (2)(0)
v2 = - (0.02)(150)/2 = - 1.5 ms–1
Here, negative sign indicates that motions ofpistol and bullet are in opposite direction.
9. A bullet of mass 20 g is fired from a gun of mass 10kg with a velocity of 180m/s. Find the velocity of the recoil of the gun . Find the force required to stop the gun before it moves 20cm. Ans: Here we shall use the conservation of momentum to calculate the recoil velocity.
Momentum of the bullet + gun before firing = 0
Momentum of the bullet + gun after firing = (20 × 10 -3) (180) + (10)(v)
‘v’ is the recoil velocity of the gun.
So, by momentum conservation,
(20 × 10 -3 )(180) + (10)(u g ) = 0
=> u g = -0.36 m/s
The negative sign indicates that the gun’s velocity is directed opposite to the velocity of the bullet.
Now,
Distance travelled before coming to rest, S = 20 cm = 0.2 m
Let ‘a’ be the acceleration with which it stops.
Using, v 2 = u 2 + 2as
=> 0 = (180) 2 + 2a × 0.2
=> a = -8100 m/s 2
So, force on the bullet, F = ma = (20 × 10 -3 ) × (-8100) = -162 N
Negative sign indicates the force is against the motion of the bullet.
10. Two billiard balls each of mass 50 g moving in opposite directions with a speed of 10m/s colloid and rebound with the same velocity .What is the impulse imparted to each ball due to other?
Ans: Impulse = change is momentum.
Initial velocity of one billiard ball, u = 10m/s Final velocity after collision, v = -10m/s
Change in momentum in one billiard ball, Δ p = m(v-u) = -1kgm/s
Similarly, change in momentum of the other billiard ball, Δ p' = +0.1kgm/s
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