If you push against a wall, the wall pushes back against you with ____ force.
1 answer:
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Answer:
a) Ffr = -0.18 N
b) a= -1.64 m/s2
c) t = 9.2 s
d) x = 68.7 m.
e) W= -12.4 J
f) Pavg = -1.35 W
g) Pinst = -0.72 W
Explanation:
a)
- While the puck slides across ice, the only force acting in the horizontal direction, is the force of kinetic friction.
- This force is the horizontal component of the contact force, and opposes to the relative movement between the puck and the ice surface, causing it to slow down until it finally comes to a complete stop.
- So, this force can be written as follows, indicating with the (-) that opposes to the movement of the object.
where μk is the kinetic friction coefficient, and Fn is the normal force.
- Since the puck is not accelerated in the vertical direction, and there are only two forces acting on it vertically (the normal force Fn, upward, and the weight Fg, downward), we conclude that both must be equal and opposite each other:
- We can replace (2) in (1), and substituting μk by its value, to find the value of the kinetic friction force, as follows:
b)
- According Newton's 2nd Law, the net force acting on the object is equal to its mass times the acceleration.
- In this case, this net force is the friction force which we have already found in a).
- Since mass is an scalar, the acceleration must have the same direction as the force, i.e., points to the left.
- We can write the expression for a as follows:
c)
- Applying the definition of acceleration, choosing t₀ =0, and that the puck comes to rest, so vf=0, we can write the following equation:
- Replacing by the values of v₀ = 15 m/s, and a = -1.64 m/s2, we can solve for t, as follows:
d)
- From (1), (2), and (3) we can conclude that the friction force is constant, which it means that the acceleration is constant too.
- So, we can use the following kinematic equation in order to find the displacement before coming to rest:
- Since the puck comes to a stop, vf =0.
- Replacing in (7) the values of v₀ = 15 m/s, and a= -1.64 m/s2, we can solve for the displacement Δx, as follows:
e)
- The total work done by the friction force on the object , can be obtained in several ways.
- One of them is just applying the work-energy theorem, that says that the net work done on the object is equal to the change in the kinetic energy of the same object.
- Since the final kinetic energy is zero (the object stops), the total work done by friction (which is the only force that does work, because the weight and the normal force are perpendicular to the displacement) can be written as follows:
f)
- By definition, the average power is the rate of change of the energy delivered to an object (in J) with respect to time.
- If we choose t₀=0, replacing (9) as ΔE, and (6) as Δt, and we can write the following equation:
g)
- The instantaneous power can be deducted from (10) as W= F*Δx, so we can write P= F*(Δx/Δt) = F*v (dot product)
- Since F is constant, the instantaneous power when v=4.0 m/s, can be written as follows:
1. A person's weight will change if they move from the Earth to the moon.
In fact, the weight of a person is given by:
where m is the mass of the person and g is the gravitational acceleration. The mass of the person, m, is the same on the Earth and on the moon, but the value of g is different on the Moon (about 1/6 of the Earth's value), so the weight also changes.
2. An astronaut is launched into space. The mass of the astronaut did not change. This is measured in Kg.
The mass of an object (or of a person, as in this case) is an intrinsec property of the object, that depends on the amount of matter inside the object: therefore, this quantity does not depend on the location of the object, so it is the same on the Earth, on the Moon and in space.
3. What is the weight of a ring tailed lemur that has a mass of 10 kg? -98 N
The weight of the lemur is given by:
where m=10 kg is the lemur's mass and g=-9.8 m/s^2 is the gravitational acceleration. Using these numbers, we find
and the negative sign simply means that the direction of the weight is downward.
4. What is the mass of the lemur from the previous question if it was on the International Space Station? 10 kg
As we said in question 1), the mass of an object does not depend on the location, so the mass of the lemur is still 10 kg, as in the previous exercise.
5. A rocket being thrust upward as the force of the fuel being burned pushes downward is an example of which of Newton's laws? Third's Newton Law
Third's Newton Law states that:
"When an object A exerts a force on an object B, then object B exerts an equal and opposite force on object A".
Applied to this case, the two objects are the fuel and the rocket. The fuel is pushed backward by the rocket, so the fuel exerts an equal and opposite force on the rocket, which then moves forward.
6. When a cannon is fired, the projectile moves forward. According to Newton's 3rd law, the cannon will want to travel backward.
Third's Newton Law states that:
"When an object A exerts a force on an object B, then object B exerts an equal and opposite force on object A".
Applied to this case, the two objects are the cannon and the projectile.The projectile is pushed forward by the cannon, so the projectile exerts an equal and opposite force on the cannon, which moves backward.
7. An object has a weight of 21,532 N on Earth. What is the mass of the object? 2,197 kg
The weight of the object is given by:
If we re-arrange the formula and we use W=21,532 N, we can find the mass of the object:
8. What is the mass of the object from the previous question if we put it on the moon? The force of gravity on the moon is 1.62 m/s2. 2,197 kg
As we said in question 4), the mass of an object does not change if we move it to another location, so its mass is still 2,197 kg.
9. How much force is exerted if a 250 kg object has an acceleration of 750 m/s2 ? 187,500 N
The force exerted on the object is given by Newton's second law:
where F is the force, m=250 kg is the mass and a=750 m/s^2 is the acceleration. By using these numbers, we find
10. A resting soccer ball moving after it is kicked is an example of which of Newton's laws? Newton's second law
Newton's second law states that when an object is acted upon unbalanced force, the object has an acceleration, given by the law
So, in this case, the ball is kicked and so an unbalanced force is applied to it, and for this reason the ball has an acceleration (in fact, it starts from rest, but then its velocity increases since it starts moving).