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?
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To determine the speed of the mass after being moved 2.0m, we need to consider the work done on the mass by the applied force.
The work done on an object is given by the equation:
Work = Force * Distance * cos(theta)
In this case, since the force and distance are both acting in the same direction horizontally, theta (the angle between the force and displacement) is 0 degrees and cos(0) = 1. Therefore, we can simplify the equation to:
Work = Force * Distance
The work done on an object is also equal to the change in its kinetic energy (KE). Therefore, we can write:
Work = Change in KE
The change in KE can be calculated using the formula:
Change in KE = (1/2) * Mass * (Final Velocity^2 - Initial Velocity^2)
Given that the mass is 25 kg and the initial velocity is 0 m/s, we need to find the final velocity.
To find the final velocity, we first need to calculate the net force acting on the mass. The net force is the difference between the applied force and the force of friction.
Net Force = Applied Force - Force of Friction
Net Force = 65 N - 15 N
Net Force = 50 N
Next, we can use Newton's second law of motion to find the acceleration of the object.
Acceleration = Net Force / Mass
Acceleration = 50 N / 25 kg
Acceleration = 2 m/s²
We can use the kinematic equation to find the final velocity:
Final Velocity^2 = Initial Velocity^2 + 2 * Acceleration * Distance
Final Velocity^2 = 0 + 2 * 2 m/s² * 2.0m
Final Velocity^2 = 8 m²/s²
Taking the square root of both sides, we can find the final velocity:
Final Velocity = √(8 m²/s²)
Final Velocity ≈ 2.83 m/s
Therefore, the speed of the mass after being moved 2.0m is approximately 2.83 m/s.