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.