A 5kg block is being pulled on a horizontal frictionless surface. The tension in the string is 30N. If the block has an initial speed of 2m/s, what is the speed after moving 10 meters?
Please help!Thanks
F=ma, so
a = 30/5 = 6 m/s^2
s = 2 + 3t^2 = 10
so, t = √(8/3) ≈ 1.633 s
v = at = 6*.1633 = 9.80 m/s
Why did the block go see a therapist? It was feeling a lot of tension! But don't worry, I'm here to help you solve this problem and bring some tension-free laughter to the equation!
To find the final speed of the block after moving 10 meters, we can use the work-energy theorem. The work done on the block by tension is equal to the change in its kinetic energy. If there is no friction, then all the work done is converted into kinetic energy.
The work done on the block can be calculated as the force multiplied by the distance the block moves. In this case, the force is the tension of 30N and the distance is 10 meters. So, the work done is 30N * 10m = 300J.
The change in kinetic energy can be calculated as the final kinetic energy minus the initial kinetic energy. Since the block starts with an initial speed of 2m/s, the initial kinetic energy is (1/2) * 5kg * (2m/s)^2 = 10J.
Using the work-energy theorem, we can write the equation:
300J = final kinetic energy - 10J
Simplifying, we find:
final kinetic energy = 300J + 10J = 310J
To calculate the final speed, we can use the equation for kinetic energy:
final kinetic energy = (1/2) * 5kg * (final speed)^2
Plugging in the value for the final kinetic energy, we get:
310J = (1/2) * 5kg * (final speed)^2
Simplifying further, we find:
310J = 2.5kg * (final speed)^2
Dividing both sides by 2.5kg, we get:
124J/kg = (final speed)^2
Taking the square root of both sides, we find:
√(124J/kg) = final speed
Calculating this, we find:
final speed ≈ 11.14 m/s
So, after moving 10 meters, the block will have a final speed of approximately 11.14 m/s.
To solve this problem, we can use the principle of work-energy.
Step 1: Determine the work done on the block.
The work done on an object is given by the equation: work = force × distance × cos(theta). In this case, the force is the tension in the string, which is 30N, and the distance is 10m. Since the force is applied horizontally and the displacement is also horizontal, the angle between the force and displacement is 0 degrees. Therefore, cos(0) = 1. Thus, the work done on the block is: work = 30N × 10m × cos(0) = 300Nm.
Step 2: Calculate the initial kinetic energy of the block.
The initial kinetic energy (KEi) of the block is given by the equation: KEi = 1/2 × mass × (initial velocity)^2. The mass of the block is 5kg, and its initial velocity is 2m/s. Substituting these values, we get: KEi = 1/2 × 5kg × (2m/s)^2 = 10J.
Step 3: Apply the work-energy principle.
According to the work-energy principle, the work done on the block is equal to the change in its kinetic energy. Therefore, the work done on the block (300J) is equal to the change in its kinetic energy (KEf - KEi). Rearranging the equation, we get: KEf = KEi + work = 10J + 300J = 310J.
Step 4: Calculate the final velocity of the block.
The final kinetic energy (KEf) of the block is given by the equation: KEf = 1/2 × mass × (final velocity)^2. Rearranging the equation, we can solve for the final velocity (v):
(final velocity)^2 = 2 × (KEf / mass)
(final velocity)^2 = 2 × (310J / 5kg)
(final velocity)^2 = 124m^2/s^2
final velocity = sqrt(124m^2/s^2) ≈ 11.1m/s.
Therefore, the final velocity of the block after moving 10 meters is approximately 11.1m/s.
To determine the final speed of the block after moving a certain distance, we can use the principle of conservation of mechanical energy.
In this case, the only external force acting on the block is the tension in the string. Since the surface is frictionless, there is no work done by friction. Therefore, the tension in the string is responsible for providing the net work done on the block.
We can calculate the work done by the tension by multiplying the tension force by the displacement. In this case, the displacement is 10 meters and the tension is 30 N:
Work = Tension * Displacement
Work = 30 N * 10 m
Work = 300 J (Joules)
The work done on an object is equal to the change in its kinetic energy. So, we can equate the work done to the change in kinetic energy:
Work = Change in Kinetic Energy
At the start, the block has an initial speed of 2 m/s. The kinetic energy at the start is given by:
Kinetic Energy initial = (1/2) * mass * velocity^2
Kinetic Energy initial = (1/2) * 5 kg * (2 m/s)^2
Kinetic Energy initial = 10 J
Let the final speed of the block be v m/s. The kinetic energy at the end is given by:
Kinetic Energy final = (1/2) * mass * velocity^2
Kinetic Energy final = (1/2) * 5 kg * v^2
Kinetic Energy final = 2.5v^2
Now we can equate the work done to the change in kinetic energy:
300 J = 2.5v^2 - 10 J
Simplifying the equation:
300 J + 10 J = 2.5v^2
310 J = 2.5v^2
Divide both sides by 2.5:
v^2 = 124 J / 2.5
v^2 = 49.6 J
Taking the square root of both sides:
v = √(49.6 J)
v ≈ 7 m/s
Therefore, the final speed of the block after moving 10 meters is approximately 7 m/s.