Statements:
1. A boy is holding a book of mass 2 kg. How much force is he applying on the book? If he moves it up with acceleration of 3 m/s², how much total force should he apply on the book?
(Ans: 19.6 N, 25.6 N)
2. A girl of mass 30 kg is running with a velocity of 4 m/s. Find her momentum.
(Ans: 120 kg·m/s)
3. A 2 kg steel ball is moving with a speed of 15 m/s. It hits a bulk of sand and comes to rest in 0.2 seconds. Find the force applied by the sand bulk on the ball.
(Ans: -150 N)
4. A 100-gram bullet is fired from a 5 kg gun. The muzzle velocity of the bullet is 20 m/s. Find the recoil velocity of the gun.
(Ans: 0.4 m/s)
5. A robotic car of 15 kg is moving at 25 m/s. Brakes are applied to stop it. If the brakes apply a constant force of 50 N, how long does the car take to stop?
(Ans: 7.5 s)
1. A boy is holding a book of mass 2 kg. How much force is he applying on the book? If he moves it up with acceleration of 3 m/s², how much total force should he apply on the book?
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First part:
The force the boy applies on the book just to hold it is equal to the weight of the book. The weight is given by:F=m⋅g
Where:
- m=2 kg (mass of the book)
- g=9.8 m/s2 (acceleration due to gravity)
F=2 kg×9.8 m/s2=19.6 N
So, the force the boy applies to hold the book is 19.6 N.
- a=3 m/s2 (upward acceleration)
Second part:
If the boy moves the book up with an acceleration of 3 m/s², the total force should also overcome the gravitational force and provide an upward acceleration. We can calculate the total force using Newton’s Second Law:Ftotal=m⋅(g+a)
Where:
Ftotal=2 kg×(9.8 m/s2+3 m/s2)
So, the total force the boy should apply is 25.6 N.
2. A girl of mass 30 kg is running with a velocity of 4 m/s. Find her momentum.
Momentum () is given by:
p=m⋅v
Where:
- m=30 kg
- v=4 m/s
p=30 kg×4 m/s=120 kg⋅m/s
So, the girl’s momentum is 120 kg·m/s.
3. A 2 kg steel ball is moving with a speed of 15 m/s. It hits a bulk of sand and comes to rest in 0.2 seconds. Find the force applied by the sand bulk on the ball.
First, find the change in momentum:
Δp=m⋅Δv
Where:
- m=2 kg
- Δv=vfinal−vinitial=0−15 m/s=−15 m/s
Δp=2 kg×(−15 m/s)=−30 kg⋅m/s
Now, use the impulse-momentum theorem, which states:
Favg⋅Δt=Δp
Where:
- Δt=0.2 s
Favg×0.2=−30 Favg=−30/0.2=−150
So, the force applied by the sand bulk on the ball is -150 N (the negative sign indicates that the force is in the opposite direction to the motion of the ball).
4. A 100-gram bullet is fired from a 5 kg gun. The muzzle velocity of the bullet is 20 m/s. Find the recoil velocity of the gun.
We can use the law of conservation of momentum. Initially, the total momentum of the system (gun + bullet) is zero. After firing, the total momentum must still be zero. Hence, the momentum of the gun and bullet must cancel each other out.
Let vgun be the recoil velocity of the gun.
mbullet⋅vbullet+mgun⋅vgun=0
Where:
- mbullet=0.1 kg (100 grams = 0.1 kg)
- vbullet=20 m/s
- mgun=5 kg
0.1 kg×20 m/s+5 kg×vgun=0 = 0 vgun=−2/5
So, the recoil velocity of the gun is -0.4 m/s (negative indicating it moves in the opposite direction).
5. A robotic car of 15 kg is moving at 25 m/s. Brakes are applied to stop it. If the brakes apply a constant force of 50 N, how long does the car take to stop?
We can use the equation of motion:
F=m⋅a
Where:
- F=50 N
- m=15 kg
First, find the acceleration:
a=F/m=50 N/15 kg=3.33 m/s2
Now, use the equation of motion:
vfinal=vinitial+a⋅t
Where:
- vfinal=0 m/s (the car stops)
- vinitial=25 m/s
0=25 m/s+(−3.33 m/s2)⋅t t=−25/−3.33=7.5 s
So, the car takes 7.5 seconds to stop.