A 3.3 kg block initially at rest is pulled to the
right along a horizontal, frictionless surface
by a constant, horizontal force of 14.8 N.
Find the speed of the block after it has
moved 3.2 m.
Answer in units of m/s.
Well, looks like we have ourselves a classic case of physics in action! To find the speed of the block after it has moved 3.2 m, we can use a few nifty equations.
First off, let's find the acceleration of the block. We can use Newton's second law, which states that the net force on an object is equal to the mass of the object multiplied by its acceleration. In this case, the net force on the block is 14.8 N and the mass of the block is 3.3 kg. So, dividing the force by the mass, we get:
acceleration = force / mass = 14.8 N / 3.3 kg
Now with the acceleration in hand, we can use another handy equation: the kinematic equation that relates displacement, initial velocity, acceleration, and time. In this case, we want to find the final velocity of the block, so we'll use the equation:
final velocity^2 = initial velocity^2 + 2 * acceleration * displacement
Since the block starts from rest, the initial velocity is 0. Plugging in the values we know, we get:
final velocity^2 = 0 + 2 * (14.8 N / 3.3 kg) * 3.2 m
Simplifying that mess, we get:
final velocity^2 = 31.313 m^2/s^2
Finally, to find the speed of the block, we take the square root of both sides of the equation:
final velocity = √(31.313 m^2/s^2)
And after some number crunching, we find that the speed of the block after it has moved 3.2 m is approximately:
final velocity ≈ 5.593 m/s
So there you have it! The block will be cruising along with a speed of about 5.593 m/s. Now you can impress all your friends with your physics knowledge. Just remember, always clown around responsibly!
To find the speed of the block after it has moved 3.2 m, we can use the work-energy principle.
The work-energy principle states that the work done on an object is equal to the change in its kinetic energy.
The work done on the block is given by the force multiplied by the distance:
Work = Force x Distance
Work = (14.8 N) x (3.2 m)
Work = 47.36 J
The change in kinetic energy is equal to the work done on the block:
Change in Kinetic Energy = Work
The initial kinetic energy of the block is zero since it is initially at rest:
Initial Kinetic Energy = 0 J
So the change in kinetic energy is equal to the final kinetic energy:
Final Kinetic Energy = Change in Kinetic Energy
We can now use the kinetic energy formula to find the final speed of the block:
Final Kinetic Energy = (1/2)mv^2
Solving for v:
v^2 = (2 x Final Kinetic Energy) / m
Plugging in the known values:
v^2 = (2 x 47.36 J) / 3.3 kg
v^2 = 30.13 J / kg
v^2 = 30.13 m^2/s^2
Taking the square root of both sides:
v = √(30.13) m/s
Rounding to the appropriate number of significant figures, the speed of the block after it has moved 3.2 m is approximately 5.49 m/s.
To find the speed of the block after it has moved 3.2 m, we can use the principle of work done.
The work done on an object is equal to the force applied on the object multiplied by the distance the object moves in the direction of the force. The work-energy theorem states that the work done on an object is equal to the change in its kinetic energy.
In this case, the force applied on the block is 14.8 N, and it moves a distance of 3.2 m in the right direction. The work done on the block is therefore:
Work = Force * Distance
= 14.8 N * 3.2 m
= 47.36 N·m or 47.36 joules
Since the work done on the block equals the change in its kinetic energy, we can equate this to the expression for kinetic energy:
Change in Kinetic Energy = 47.36 J
The formula for kinetic energy is:
Kinetic Energy = 0.5 * mass * velocity^2
Since the block starts from rest, its initial kinetic energy is zero. Therefore, the final kinetic energy (i.e., the work done on the block) is equal to its change in kinetic energy:
0.5 * mass * velocity^2 = 47.36 J
Substituting the known values:
0.5 * 3.3 kg * velocity^2 = 47.36 J
Rearranging the equation to solve for velocity:
velocity^2 = (2 * 47.36 J) / 3.3 kg
velocity^2 = 143.879 m^2/s^2
Taking the square root of both sides to solve for velocity:
velocity = √(143.879 m^2/s^2)
Calculating the square root gives us the final answer:
velocity ≈ 12.005 m/s
Therefore, the speed of the block after it has moved 3.2 m is approximately 12.005 m/s.