a 33 kg lawnmower is pulled by a 100N force on flat ground. The handle makes a 10 degree angle with the ground. The coefficient of friction between grass and lawnmower wheels is 0.10.
Calculate normal force, force of friction and acceleration
I need help
a man pushes a lawn mower 50 feet in 5 second by exerting a force of 30 pounds at an angle of 53
To calculate the normal force, force of friction, and acceleration, we need to break down the forces acting on the lawnmower.
1. Normal Force (N):
The normal force is the force exerted by the ground on the lawnmower perpendicular to the ground. In this case, the normal force counters the weight of the lawnmower.
The weight (mg) of the lawnmower can be calculated by multiplying its mass (33 kg) by the acceleration due to gravity (9.8 m/s^2):
Weight (mg) = 33 kg * 9.8 m/s^2 = 323.4 N
Since the lawnmower is on flat ground, the normal force is equal in magnitude and opposite in direction to the weight, so the normal force is 323.4 N.
2. Force of Friction (Ff):
The force of friction is the force that opposes the motion of the lawnmower. It can be calculated using the formula Ff = μ * N, where μ is the coefficient of friction (0.10) and N is the normal force (323.4 N):
Ff = 0.10 * 323.4 N = 32.34 N
3. Acceleration:
To calculate the acceleration, we need to consider the forces acting on the lawnmower. The force exerted by the person pulling the lawnmower is the driving force, and it can be calculated using the force's component in the direction of motion. The angle between the handle and the ground is 10 degrees, so the component of the force in the direction of motion is Fcosθ, where θ is the angle (10 degrees) and F is the force applied (100 N):
Driving force = Fcosθ = 100 N * cos(10°) = 98.5 N
Now, considering friction, the net force acting on the lawnmower is the difference between the driving force and the force of friction:
Net force = Driving force - Force of friction = 98.5 N - 32.34 N = 66.16 N
Finally, we can calculate the acceleration using Newton's second law formula, F = ma, where F is the net force and a is the acceleration:
a = F/m = 66.16 N / 33 kg = 2.005 m/s^2 (approximately)
Therefore, the normal force is 323.4 N, the force of friction is 32.34 N, and the acceleration is approximately 2.005 m/s^2.
notice there is a slight upward force on the lawnmower, this reduces weight and friction.
upwoard force= 100*sin10
friction= (33*g-100sin10)*mu
Net horizontal force=100cos10-frictonabove
acceleration=nethorizontalforce/mass