A 25 kg mass is on a level, rough surface where the force of friction is a constant 15 N. A horizontal applied force of 65 N acts on the mass. The mass is initially at rest.
What speed does that mass have after being moved 2.0m?
V = sqrt(2aX)
where a is the acceleration and X is the distance it has moved from a stationary start.
The net force acting horizontally on the block is F = 50 N. Thus a = F/m = 50/25 = 2 m/s^2
V = sqrt(2*2*2) = sqrt8 = 2.83 m/s
To find the speed of the mass after being moved 2.0m, we need to use the laws of motion. First, let's calculate the work done by the applied force.
Work done = Force × Distance × cos(θ)
Where:
Force = 65 N (applied force)
Distance = 2.0 m (distance moved)
θ = angle between the force and the displacement. Since the force is horizontal and the displacement is horizontal, θ = 0°.
Work done = 65 N × 2.0 m × cos(0°)
= 130 N·m
Now, let's calculate the work done against friction.
Work done against friction = Force of friction × Distance × cos(θ)
Where:
Force of friction = 15 N (constant force of friction)
Distance = 2.0 m (distance moved)
θ = angle between the force of friction and the displacement. Since the force of friction always opposes motion, θ = 180°.
Work done against friction = 15 N × 2.0 m × cos(180°)
= -30 N·m
Note: The negative sign indicates that the work is done against the motion.
Next, let's calculate the net work done on the mass.
Net work done = Work done - Work done against friction
= 130 N·m - (-30 N·m)
= 160 N·m
Now, let's calculate the change in kinetic energy of the mass using the work-energy theorem.
Change in kinetic energy = Net work done
Since the mass is initially at rest, the initial kinetic energy is 0.
Final kinetic energy = Change in kinetic energy + Initial kinetic energy
= Net work done + 0
= 160 N·m
Finally, let's calculate the speed of the mass.
Final kinetic energy = (1/2) × mass × velocity^2
Rearranging the equation:
velocity^2 = (2 × Final kinetic energy) / mass
velocity^2 = (2 × 160 N·m) / 25 kg
velocity^2 = 6.4 m^2/s^2
Taking the square root of both sides:
velocity = √(6.4 m^2/s^2)
velocity ≈ 2.53 m/s
Therefore, the speed of the mass after being moved 2.0m is approximately 2.53 m/s.