A 17.9 kg block is dragged over a rough, horizontal
surface by a constant force of 119 N
acting at an angle of 30◦
above the horizontal.
The block is displaced 40.7 m, and the
coefficient of kinetic friction is 0.111. what is the final speed
first, the lifting force: 119N*sin30
now the normal force= mg-119*sin30
now the friction: mu* (mg-119Sin30)
pulling force: 119Cos30
net force=mass*acceleration
pullingforce-friction=mass(a)
solve for acceleration a.
Finally,
Vf^2=Vi^2+2ad solve for Vf
To find the final speed of the block, we can use the work-energy principle. The work done by the applied force is equal to the change in kinetic energy of the block.
1. First, let's calculate the work done by the applied force. The component of force parallel to the displacement of the block will do work, while the component perpendicular to the displacement will not contribute to the work done.
Force parallel to displacement = 119 N * cos(30°)
Work done by the applied force = (119 N * cos(30°)) * 40.7 m
2. Next, let's calculate the work done by friction. The work done by friction is equal to the force of friction multiplied by the displacement.
Force of friction = coefficient of friction * normal force
Normal force = mass * gravitational acceleration
Force of friction = (0.111) * (17.9 kg * 9.8 m/s²)
Work done by friction = (0.111 * 17.9 kg * 9.8 m/s²) * 40.7 m
3. The total work done is the sum of the work done by the applied force and the work done by friction.
Total work done = Work done by the applied force - Work done by friction
4. Finally, we can equate the total work done to the change in kinetic energy to find the final speed of the block.
Change in kinetic energy = Total work done / mass of the block
Final speed = square root((2 * (Total work done / mass of the block)))
By substituting the values into the equations, we can calculate the final speed of the block.
To find the final speed of the block, we can use the principle of work and energy.
First, let's determine the work done by the constant force acting on the block. The work done by the force can be calculated using the formula:
Work = Force * Distance * cosθ
Where:
- Force is the magnitude of the force acting on the block (119 N),
- Distance is the displacement of the block (40.7 m),
- θ is the angle between the force and the displacement (30 degrees).
Plugging in the values, we get:
Work = 119 N * 40.7 m * cos(30°)
Next, we need to calculate the work done against friction. The work done against friction can be determined using the formula:
Work against friction = Force of friction * Distance
Where:
- Force of friction is the product of the coefficient of kinetic friction (μk) and the normal force.
- Distance is the displacement of the block (40.7 m).
To find the normal force, we need to consider the downward force due to gravity acting on the block. The normal force is equal in magnitude and opposite in direction to the force due to gravity (weight).
Weight = mass * acceleration due to gravity
Where:
- Mass is the mass of the block (17.9 kg),
- Acceleration due to gravity is approximately 9.8 m/s^2.
Normal force = Weight = mass * acceleration due to gravity
Using the given values, we can calculate the normal force. Once we have the normal force, we can calculate the force of friction using the formula:
Force of friction = coefficient of kinetic friction * normal force
Once we have the force of friction, we can calculate the work done against friction using the formula mentioned earlier:
Work against friction = Force of friction * Distance
Now that we have the work done by the force and the work done against friction, we can calculate the net work done on the block:
Net work done = Work - Work against friction
According to the work-energy principle, the net work done on an object is equal to the change in its kinetic energy.
Net work done = Change in kinetic energy
Since the block starts from rest, its initial kinetic energy is zero:
Net work done = Final kinetic energy
Using the formula for kinetic energy:
Final kinetic energy = (1/2) * mass * final velocity^2
We can rearrange the formula as follows to solve for the final velocity:
Final velocity = sqrt((2 * Net work done) / mass)
Plugging in the values, we can solve for the final velocity of the block.