You slide a box of books at constant speed up a 30° ramp, applying a force of 200 n directed up the slope. the coefficient of sl
2 answers:
The box is moving at constant speed, so acceleration=0 and the equation of the forces acting on the box along the ramp becomes:
(1)
where F=200 N is the force that pushes the box, Ff is the frictional force, and Wp is the component of the weight parallel to the ramp.
The frictional force can be written as
where is the coefficient of friction, m is the mass of the box,
is the frictional force and
is the angle of the ramp.
The component of the weight along the ramp is
Substituting this into eq.(1), we have
and we can find the mass of the box:
Now we can also find the work done on the box. this is given by the gain in potential energy of the box, since there is no change in kinetic energy (the speed of the box is constant). Since the box has risen vertically by 1 m, the gain in potential energy (and the work done) is
So, the two answers are
(a) 304.8 J
(b) 31.1 kg
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The total momentum before and after the collision must be conserved.
- Let's start from the end: at this point, both cart and laundry bag are moving together, with a total mass of (m1+m2) and velocity 2.6 m/s. Therefore, the total momentum is
- The momentum must be conserved, so the initial momentum must be equal to this value:
- At the beginning, the cart is stationary, so its momentum is zero. There is only one momentum, the one of the bag, which has a mass of 20 kg and unknwon velocity vi:
- So, using the conservation of momentum we find
and from this, the initial velocity of the laundry bag:
- Let's start from the end: at this point, both cart and laundry bag are moving together, with a total mass of (m1+m2) and velocity 2.6 m/s. Therefore, the total momentum is
- The momentum must be conserved, so the initial momentum must be equal to this value:
- At the beginning, the cart is stationary, so its momentum is zero. There is only one momentum, the one of the bag, which has a mass of 20 kg and unknwon velocity vi:
- So, using the conservation of momentum we find
and from this, the initial velocity of the laundry bag:
Answer:
a)
b)
If we analyze the two values obtained for the centripetal acceleration we see that are similar. Based on this we can say that the centripetal force would be similar to the gravitational force between the Earth and Moon.
Explanation:
1) Notation and important concepts
Centripetal acceleration is defined as "The acceleration experienced while in uniform circular motion. It always points toward the center of rotation and is perpendicular to the linear velocity."
Angular frequency is defined as "(ω), or radial frequency, measures angular displacement per unit time and the units are usually degrees (or radians) per second. "
T = 27.3 d represent the time required by the Earth around an specific point given in the problem
G= universal constant
M= represent the mass of the Moon=7.35x10^{22}kg
2) Part a
(1)
The Earth-Moon Distance Is (average Value) and both rotates at a point located about 4700 km from the center of Earth, so the radius for this case would be the difference between these two values
Since we have the radius now we can replace into equation (1)
And the acceleration due to the Moon's gravity would be at the point required.
3)Part b
For this case we can find the centripetal acceleration from this formula:
(2)
But on this case we don't have the angular frequency so we can find it with this formula
(3)
But since the period is on days we need to convert that into seconds
Replacing the value into equation (3) we got:
Now we can find the centripetal acceleration with the equation (2), the new radius on this case since our reference is the Earth and the point is located 4700km=4700000m from the center of Earth then the new value for the radius would be r=4700000m
If we analyze the two values obtained for the centripetal acceleration we see that are similar. Based on this we can say that the centripetal force would be similar to the gravitational force between the Earth and Moon.