A 8.22 kg block initially at rest is pulled to the
right along a horizontal, frictionless surface by
a constant, horizontal force of 16.8 N.
Find the speed of the block after it has
moved 2.3 m.
Answer in units of m/s
First compute the acceleration,
a = F/m = 2.044 m/s^2
Then use
V(final) = sqrt(2 a X)
where X is the distance travelled.
You could also use:
Work done on block = F*X
= final kinetic energy,
= (1/2)M Vfinal^2.
and then solve for Vfinal.
Vfinal = sqrt[2*(F/M)*x]
You will get the same result.
To find the speed of the block after it has moved 2.3 m, you can use the equation:
Work = Force * Distance
Since there is no friction, all the work done by the force will be converted into kinetic energy.
The work done by the force is given by:
Work = Force * Distance
Plugging in the values:
Work = 16.8 N * 2.3 m
Work = 38.64 N·m
Since the work done is equal to the change in kinetic energy, we can equate it to the following equation:
Work = (1/2) * mass * velocity^2
Substituting the values:
38.64 N·m = (1/2) * 8.22 kg * velocity^2
Now, we can solve for velocity:
velocity^2 = (38.64 N·m) / ((1/2) * 8.22 kg)
Simplifying:
velocity^2 = 9.38 m^2/s^2
Taking the square root of both sides:
velocity = sqrt(9.38) m/s
Finally, we can calculate the speed of the block after it has moved 2.3 m:
velocity ≈ 3.06 m/s
Therefore, the speed of the block after it has moved 2.3 m is approximately 3.06 m/s.
To find the speed of the block after it has moved 2.3 m, we can use the concept of work and energy.
First, let's calculate the work done on the block. The work done on an object is given by the formula:
Work = Force * Distance * cos(θ)
Here, the force applied is 16.8 N and the distance moved by the block is 2.3 m. Since the force is applied horizontally and the displacement is also horizontal, the angle (θ) between the force and displacement is 0 degrees, which means cos(θ) = 1. Hence, the work done is:
Work = 16.8 N * 2.3 m * 1 = 38.64 J (joules)
According to the work-energy principle, the work done on an object is equal to the change in its kinetic energy. So in this case, the work done on the block is equal to the change in its kinetic energy:
Work = ΔKE
The initial kinetic energy (KE) of the block is 0 J, as it is initially at rest. Therefore:
38.64 J = ΔKE
Now, let's solve for the change in kinetic energy (ΔKE) by rearranging the equation:
ΔKE = 38.64 J
Since the block is initially at rest, its final kinetic energy (KEf) will be equal to the change in kinetic energy (ΔKE):
KEf = ΔKE = 38.64 J
The kinetic energy (KE) of an object is given by the formula:
KE = 0.5 * mass * velocity^2
We can rearrange this equation to solve for the velocity (v):
v = sqrt(2 * KE / mass)
Plugging in the values, we have:
v = sqrt(2 * 38.64 J / 8.22 kg)
v = sqrt(94.872 / 8.22) m/s
v = sqrt(11.54) m/s
v ≈ 3.39 m/s
Therefore, the speed of the block after it has moved 2.3 m is approximately 3.39 m/s.
First compute the acceleration,
a = F/m = 2.044 m/s^2
V = s