# A man pushes 100.0 N on the handle of a 40.0 kg lawnmower. The applied force is in the same direction as the handle, which is tilted 35.0° relative to horizontal. The coefficient of kinetic friction is 0.10. Find the amount of acceleration.

## To find the amount of acceleration, we need to first determine the net force acting on the lawnmower.

Step 1: Resolve the applied force into horizontal and vertical components.

The applied force of 100.0 N can be resolved into horizontal and vertical components as follows:

F_horizontal = F_applied * cos(θ)

F_horizontal = 100.0 N * cos(35.0°)

F_vertical = F_applied * sin(θ)

F_vertical = 100.0 N * sin(35.0°)

Step 2: Determine the force of friction.

The force of friction can be calculated using the formula:

F_friction = μ * F_normal

where:

μ is the coefficient of kinetic friction

F_normal is the normal force, which is equal to the weight of the lawnmower (mass * acceleration due to gravity)

F_normal = m * g

F_normal = 40.0 kg * 9.8 m/s²

F_friction = 0.10 * (40.0 kg * 9.8 m/s²)

Step 3: Calculate the net horizontal force.

The net horizontal force is the difference between the horizontal component of the applied force and the force of friction:

F_net_horizontal = F_horizontal - F_friction

Step 4: Determine the acceleration.

Finally, we can calculate the acceleration using Newton's second law:

F_net_horizontal = m * a

Solving for acceleration:

a = F_net_horizontal / m

where:

F_net_horizontal is the net horizontal force calculated in step 3

m is the mass of the lawnmower

Substitute the values into the formula and calculate the acceleration.