A block of mass 35 kg moves on the horizontal surface. If initially at rest whwat is the speed of the block after moving a distance of 6m when G=32?
To find the speed of the block after moving a distance of 6m, we need to apply Newton's second law of motion.
Step 1: Identify the given information:
- Mass of the block (m) = 35 kg
- Distance traveled (d) = 6 m
- Acceleration due to gravity (g) = 32 m/s²
Step 2: Calculate the work done:
The work done is given by the equation: Work = Force × Distance
In this case, the gravitational force acting on the block is given by: Force = Mass × Acceleration due to gravity
So, Force = m × g = 35 kg × 32 m/s²
Now, calculate the work done:
Work = Force × Distance = (35 kg × 32 m/s²) × 6 m
Step 3: Calculate the kinetic energy:
The work done is equal to the change in kinetic energy. Kinetic energy is given by the equation: Kinetic Energy = 0.5 × Mass × Velocity²
Let's assume the initial velocity of the block is zero and the final velocity is v (which we are trying to find).
So, the work done (calculated in step 2) is equal to the change in kinetic energy:
(35 kg × 32 m/s²) × 6 m = 0.5 × 35 kg × v²
Step 4: Solve for v (velocity):
Divide both sides of the equation by 0.5 × 35 kg to isolate v²:
v² = [(35 kg × 32 m/s²) × 6 m] / (0.5 × 35 kg)
Simplify:
v² = (35 kg × 32 m/s² × 6 m) / (0.5 × 35 kg)
Cancel out the terms:
v² = 32 m/s² × 6 m / 0.5
Multiply:
v² = 192 m²/s² / 0.5
v² = 384 m²/s²
Finally, take the square root of both sides to find the velocity (v):
v = √(384 m²/s²)
v ≈ 19.60 m/s
Therefore, the speed of the block after moving a distance of 6m is approximately 19.60 m/s.