The speed of the cat
1 answer:
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The magnitude of the friction force is 25 N
Explanation:
To solve this problem, we just have to analyze the forces acting on the block along the horizontal direction. We have:
- The horizontal component of the pulling force,
, where F = 50 N is the magnitude and
is the angle between the direction of the force and the horizontal; this force acts in the forward direction
- The force of friction,
, acting in the backward direction
According to Newton's second law, the net force acting on the block in the horizontal direction must be equal to the product between the mass of the block and its acceleration:
where
m is the mass of the block
is the horizontal acceleration
However, the block is moving at constant speed, so the acceleration is zero:
So the equation becomes
(1)
The net force here is given by
(2)
And so, by combining (1) and (2), we find the magnitude of the friction force:
Learn more about force of friction:
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Answer:
The total distance is 130.2 [m]
Explanation:
In order to solve this problem we must use the expressions of kinematics. The clue to solve this problem is that the cart starts from rest, i.e. its initial speed is zero.
where:
Vf = final velocity [m/s]
Vo = initial velocity = 0
a = acceleration = 3 [m/s²]
t = time = 8[s]
Vf = 0 + (3*8)
Vf = 24 [m/s]
With this velocity we can calculate the displacement using the following expression.
where
x = distance traveled [m]
24² = 0 + (2*3*x)
x = 576/(6)
x = 96 [m]
Note: The positive sign in the equations is because the car is accelerating, it means its velocity is increasing.
The other important clue to solve this problem in the second part is that the final velocity is now the initial velocity.
We must calculate the final velocity.
Vf = final velocity [m/s]
Vi = initial velocity = 24 [m/s]
a = desacceleration = 1.6 [m/s²]
t = time = 15 [s]
Vf = 24 - (1.6*15)
Vf = 21.6 [m/s]
With this velocity, we can calculate the displacement using the following expression.
where
x = distance traveled [m]
21.6² = 24² - (2*1.6*x)
x = 109.44/(3.2)
x = 34.2 [m]
Note: The negative sign in the equations is because the car is desaccelerating, it means its velocity is decreasing.
Therefore the total distance is Xt = 34.2 + 96 = 130.2 [m].