A person pushes a 11.0 kg lawn mower at constant speed with a force of 76.0 N directed along the handle, which is at an angle of è = 41.0° to the horizontal. Calculate the normal force exerted vertically upward on the mower by the ground. Calculate the force the person must exert on the lawn mower to accelerate it from rest to 1.3 m/s in 2.0 seconds (assuming the same retarding force).
W = mg = 11kg * 9.8N/kg = 107.8N. =
Weight of lawn mower.
Fm = 107.8N @ 0deg. = Force of mower.
Fp = Fh = 107.8sin(0) = 0 = Force parallel to ground = Hor comp.
Fv = 107.8cos(0) = 107.8N. = Force perpendicular to ground.
a. Fn = Fv + Fap*sin41,
Fn = 107.8 + 76sin41 = 157.7N.=Normal force upward from ground.
b. a = (Vf - Vo) / t,
a = (1.3 - 0) / 2 = 0.65m/s^2.
Fap = 76 + ma = 76 + 11*0.65 = 83.15N.
= Force applied.
To calculate the normal force exerted vertically upward on the mower by the ground, we need to resolve the force applied by the person into its horizontal and vertical components.
Given:
Mass of the lawn mower (m) = 11.0 kg
Force applied by the person (F) = 76.0 N
Angle between the handle and the horizontal (θ) = 41.0°
To calculate the normal force (N), we need to find its vertical component. We can use trigonometry to find this component:
Vertical component of force (F_y) = F * sin(θ)
= 76.0 N * sin(41.0°)
≈ 48.69 N
The normal force (N) is equal in magnitude but opposite in direction to the vertical component of the applied force. So:
N = -F_y
= -48.69 N
≈ -48.69 N (upward)
Therefore, the normal force exerted vertically upward on the mower by the ground is approximately 48.69 N.
Next, to calculate the force the person must exert on the lawn mower to accelerate it from rest to 1.3 m/s in 2.0 seconds, we can use Newton's second law of motion:
Force (F') = mass (m) * acceleration (a)
Given:
Initial velocity (v_i) = 0 m/s
Final velocity (v_f) = 1.3 m/s
Time (t) = 2.0 s
Acceleration (a) can be calculated using the formula:
a = (v_f - v_i) / t
Substituting the given values:
a = (1.3 m/s - 0 m/s) / 2.0 s
≈ 0.65 m/s²
Now, we can calculate the force required using Newton's second law:
F' = m * a
= 11.0 kg * 0.65 m/s²
≈ 7.15 N
Therefore, the force the person must exert on the lawn mower to accelerate it from rest to 1.3 m/s in 2.0 seconds is approximately 7.15 N.