A 8.9 kg block initially at rest is pulled to the right along a horizontal, frictionless surface by a constant, horizontal force of 12.1 N.
Find the speed of the block after it has moved 3.3 m.
Answer in units of m/s
F = m a
solve for a
then
v = 0 + a t
to get t:
d = 3.3 = (1/2) a t^2
F=MA>
sqrt(2AX)
distance is X
To find the speed of the block after it has moved 3.3 m, we can use the work-energy principle. The work done on the block is equal to the change in its kinetic energy.
The work done on the block can be calculated using the equation:
Work = Force × Distance
Given that the force applied is 12.1 N and the distance moved is 3.3 m, we can find the work done:
Work = 12.1 N × 3.3 m = 39.93 J
Next, we can use the work-energy principle:
Work = Change in Kinetic Energy
The initial kinetic energy of the block is zero since it is at rest. Therefore, the change in kinetic energy is equal to the final kinetic energy.
Let's assume the final speed of the block is v.
Change in Kinetic Energy = 1/2 × Mass × (Final Speed)^2
Given that the mass of the block is 8.9 kg, we can substitute the values into the equation:
39.93 J = 1/2 × 8.9 kg × (v)^2
To solve for the final speed (v), we can rearrange the equation:
v^2 = 39.93 J × 2 / (8.9 kg)
v^2 = 8.93 m^2/s^2
Taking the square root of both sides of the equation, we find:
v = √(8.93 m^2/s^2) = 2.99 m/s
Therefore, the speed of the block after it has moved 3.3 m is approximately 2.99 m/s.
To find the speed of the block after it has moved 3.3 m, we can use the concept of work and energy. The work done on an object is equal to the change in its kinetic energy.
The formula for work is given by:
Work = Force × Distance × cos(θ)
In this case, the force is the constant, horizontal force applied to the block, which is 12.1 N. The distance is the displacement of the block, given as 3.3 m, and the angle θ is 0° since the force and displacement are in the same direction. Thus, cos(0°) = 1.
Work = 12.1 N × 3.3 m × 1
The work done on the block is equal to its change in kinetic energy. Initially, the block is at rest, so its initial kinetic energy is zero.
Work = Change in Kinetic Energy
12.1 N × 3.3 m × 1 = (1/2) × mass × (final velocity)^2
Rearranging the equation to solve for the final velocity:
(final velocity)^2 = (2 × Work) / mass
The mass of the block is given as 8.9 kg, so we can substitute the known values into the equation:
(final velocity)^2 = (2 × 12.1 N × 3.3 m) / 8.9 kg
(final velocity)^2 = 94.98 N・m / 8.9 kg
(final velocity)^2 = 10.68 m²/s²
To find the final velocity, we take the square root of both sides of the equation:
final velocity = √(10.68 m²/s²) ≈ 3.27 m/s
Therefore, the speed of the block after it has moved 3.3 m is approximately 3.27 m/s.