Answer:
You want to use a rope to pull a 10-kg box of books up a plane inclined 30∘ above the horizontal. The coefficient of kinetic fri
ction is 0.29. The rope pulls parallel to the incline.
What force do you need to exert on the rope if you want to pull the box with a constant acceleration of 0.50 m/s2 up the plane?
What force do you need to exert on the rope if you want to pull the box with a constant acceleration of 0.50 m/s2 up the plane?
1 answer:
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Answer:
, assuming that the gravitational field strength is
.
Explanation:
Notice that both the speed and the direction of motion of this block are constant. In other words, the velocity of this block is constant.
By Newton's Second Law, the net force on this block would be . External forces on this block should be balanced. Thus, the magnitude of the (downward) weight of this block should be equal to the magnitude of the (upward) force that the boy applies on this block.
Let denote the mass of this block. It is given that
. The weight of this block would be:
.
Hence, the force that the boy applies on this block would be upward with a magnitude of .
The mechanical work that a force did is equal to the product of:
- the magnitude of the force, and
- the displacement of the object in the direction of the force.
The displacement of this block (upward by ) is in the same direction as the (upward) force that this boy had applied. Thus, the work that this boy had done would be the product of:
- the magnitude of the force that this boy exerted,
, and
- the displacement of this block in the direction,
.
.
The frequency of a simple harmonic oscillator such as a spring-mass system is given by
where
k is the spring constant
m is the mass attached to the spring.
Re-arranging the formula, we get:
and since we know the constant of the spring:
and the frequency of oscillation:
f=1.00 Hz
we can find the value of the mass attached to it:
where
k is the spring constant
m is the mass attached to the spring.
Re-arranging the formula, we get:
and since we know the constant of the spring:
and the frequency of oscillation:
f=1.00 Hz
we can find the value of the mass attached to it: