A 6.00 kg block located on a horizontal frictionless floor is pulled by a cord that exerts a force F=14.1 N at an angle θ= 19.0° above the horizontal, as shown.
What is the speed of the block 3.50 seconds after it starts moving?
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To find the speed of the block 3.50 seconds after it starts moving, we need to use Newton's second law of motion and kinematic equations.
First, let's find the acceleration of the block. The force exerted by the cord can be resolved into horizontal and vertical components. The horizontal component of force is Fcos(θ), and since there is no friction acting horizontally, this force will cause the acceleration of the block.
Fcos(θ) = 14.1 N * cos(19.0°) = 13.30 N
Using Newton's second law, F = ma, where F is the net force acting on the block and a is the acceleration, we can substitute the force and solve for acceleration.
13.30 N = 6.00 kg * a
a = 13.30 N / 6.00 kg = 2.22 m/s²
Now that we know the acceleration, we can find the speed of the block after 3.50 seconds using the following kinematic equation:
v = u + at
where v is the final velocity, u is the initial velocity (which is zero because the block starts from rest), a is the acceleration, and t is time.
v = 0 + (2.22 m/s²) * (3.50 s)
v = 7.77 m/s
Therefore, the speed of the block 3.50 seconds after it starts moving is 7.77 m/s.