A 5.86 kg block initially at rest is pulled to the

right along a horizontal surface by a constant,
horizontal force of 14.4 N. The coefficient of
kinetic friction is 0.14.
The acceleration of gravity is 9.8 m/s
2
.
Find the speed of the block after it has
moved 4.98 m.
Answer in units of m/s.

12

To find the speed of the block after it has moved a certain distance, we need to first determine the net force acting on the block and then use it to calculate the acceleration. Once we know the acceleration, we can use the kinematic equation to find the final speed.

1. Determine the net force:
The net force on the block is the difference between the applied force and the force of friction. The force of friction can be calculated using the equation: Frictional force = coefficient of kinetic friction × normal force, where the normal force is equal to the weight of the block (mass × acceleration due to gravity). So, the force of friction can be calculated as follows:
Frictional force = (coefficient of kinetic friction) × (mass × acceleration due to gravity)

2. Calculate the net force:
The net force can be determined as the applied force minus the force of friction:
Net force = Applied force - Frictional force

3. Calculate the acceleration:
Use Newton's second law, F = ma, where F is the net force and m is the mass of the block, to find the acceleration:
Acceleration = Net force / Mass

4. Calculate the final speed:
Use the kinematic equation, vf^2 = vi^2 + 2aΔd, where vf is the final velocity, vi is the initial velocity (which is 0 since the block starts from rest), a is the acceleration, and Δd is the distance traveled:
vf = sqrt(2aΔd)

Now, let's calculate the final speed of the block after it has moved 4.98m.

Given:
Mass of the block (m) = 5.86 kg
Applied force (F) = 14.4 N
Coefficient of kinetic friction (μ) = 0.14
Acceleration due to gravity (g) = 9.8 m/s^2
Distance traveled (Δd) = 4.98 m

1. Calculate the force of friction:
Frictional force = (coefficient of kinetic friction) × (mass × acceleration due to gravity)
Frictional force = 0.14 × (5.86 kg × 9.8 m/s^2)

2. Calculate the net force:
Net force = Applied force - Frictional force

3. Calculate the acceleration:
Acceleration = Net force / Mass

4. Calculate the final speed:
vf = sqrt(2aΔd)

By plugging in the given values, you can calculate the final speed of the block after it has moved 4.98 m.