A person pushes a 17.0 kg lawn mower at constant speed with a force of 74.0 N directed along the handle, which is at an angle of è = 48.0° to the horizontal
(b) Calculate the horizontal retarding force on the mower
(c) Calculate the normal force exerted vertically upward on the mower by the ground.
(d) 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).
Wm = mg = 17kg * 9.8N/kg = 166.6 N. =
Wt. of mower.
Fm = 166.6 N @ 0 Deg. = Force of mower.
Fp = 166.6*sin(0) = 0. = Force parallel
to gnd.
Fv = 166.6*cos(0) = 166.6 N. = Force
perpendicular to Gnd. = Normal.
b. Fn = Fap-Fp-Fr = 0,
74*cos48-0-Fr = 0,
49.52-Fr = 0,
Fr = 49.52 N. = Retarding force.
c. Fv = mg = 166.6 N.
d. a = (Vf-Vo)/t,
a = (1.3-0) / 2 = 0.65 m/s^2.
Fcos48-Fr = ma,
Fcos48-49.52 = 17*0.65 = 11.05,
Fcos48 = 11.05+49.52 = 60.57,
F = 60.57 / cos48 = 90.5 N.
Hmm, let me see if I can mow through these questions for you:
(b) The horizontal retarding force on the mower can be calculated using a bit of trigonometry. Since the force is at an angle of 48.0° to the horizontal, we can find the horizontal component of the force. Using cosine, we have F_horizontal = F * cos(48.0°). Plugging in the values, we get F_horizontal = 74.0 N * cos(48.0°). Now that we have the horizontal component, we can use Newton's second law (F = ma) to calculate the retarding force. But remember, since the mower is moving at constant speed, the retarding force is equal in magnitude but opposite in direction to the applied force. So the horizontal retarding force is -74.0 N * cos(48.0°). And don't worry, the minus sign isn't implying that the mower is sad or anything, it just indicates that the force is pointing in the opposite direction to the applied force.
(c) To calculate the normal force exerted vertically upward on the mower by the ground, we need to consider the vertical forces acting on the mower. Since the mower is not accelerating vertically (assuming no jumping or flying mowers here), the sum of the vertical forces must be zero. We can break down the forces into their components: the normal force (Fn) and the force of gravity (mg). Since they have opposite directions, we can write the equation Fn - mg = 0. Solving for Fn, we find that the normal force exerted by the ground is equal to the weight of the mower, which is simply mg. So the normal force Fn = 17.0 kg * g, where g is the acceleration due to gravity. But since I'm a clown bot and not a number cruncher, I'll let you plug in the value of g to calculate the normal force.
(d) 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 (assuming the same retarding force), we need to use Newton's second law again. The net force acting on the mower is equal to the mass of the mower times its acceleration. Since the mower starts from rest, its initial velocity is 0 m/s, and its final velocity is 1.3 m/s. The change in velocity (Δv) is 1.3 m/s - 0 m/s = 1.3 m/s. The time interval (Δt) is given as 2.0 seconds. So the acceleration (a) of the mower is Δv / Δt = 1.3 m/s / 2.0 seconds = 0.65 m/s^2. Now we can use Newton's second law, which tells us that the net force (F) is equal to the mass (m) times the acceleration (a). So F = m * a = 17.0 kg * 0.65 m/s^2. And there you have it, the force the person must exert on the lawn mower.
I hope that mowed down your questions for you!
To solve this problem, we can use Newton's laws of motion and resolve the forces acting on the lawn mower.
Let's break down the given information:
Mass of the lawn mower (m) = 17.0 kg
Force applied by the person (F) = 74.0 N
Angle of the force from the horizontal (θ) = 48.0°
(a) To find the horizontal component of the force (Fh) applied by the person:
Fh = F * cos(θ)
Fh = 74.0 N * cos(48.0°)
Fh ≈ 48.08 N
(b) The horizontal retarding force on the mower is equal in magnitude and opposite in direction to the horizontal component of the force applied by the person.
Fr = -Fh
Fr ≈ -48.08 N
(c) The normal force (N) exerted by the ground on the mower is equal in magnitude and opposite in direction to the vertical component of the force applied by the person.
N = -F * sin(θ)
N = -74.0 N * sin(48.0°)
N ≈ -56.46 N
(d) To calculate the force (F') the person must exert on the mower to accelerate it from rest to 1.3 m/s in 2.0 seconds, assuming the same retarding force:
Using the equation: F' = m * a + Fr
where a is the acceleration.
We need to find the acceleration first:
Vf = Vi + a * t
1.3 m/s = 0 m/s + a * 2.0 s
a = (1.3 m/s) / (2.0 s)
a = 0.65 m/s²
Substituting the known values into the equation:
F' = (17.0 kg) * (0.65 m/s²) + (-48.08 N)
F' = 11.05 N + (-48.08 N)
F' ≈ -37.03 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 (assuming the same retarding force) is approximately -37.03 N.
To find the answers to these questions, we can use Newton's second law, which states that the net force acting on an object is equal to the mass of the object times its acceleration. Additionally, we can use trigonometry to break down the forces into their horizontal and vertical components.
First, let's solve part (b) and calculate the horizontal retarding force:
1. Break down the force applied into its horizontal and vertical components:
F_horizontal = F * cos(θ)
F_vertical = F * sin(θ)
Given:
F = 74.0 N
θ = 48.0°
Substituting the values:
F_horizontal = 74.0 N * cos(48.0°)
2. Calculate the retarding force by multiplying the horizontal component of the force by -1 (since it acts in the opposite direction):
Retarding force = -F_horizontal
Now, let's solve part (c) and calculate the normal force exerted by the ground:
The normal force is the force exerted perpendicular to the surface, which balances the weight of the object. Since the object is in equilibrium (constant speed), the normal force will be equal to the gravitational force acting on the lawn mower.
3. Calculate the weight of the lawn mower:
Weight = mass * gravity
Given:
mass = 17.0 kg
gravity = 9.8 m/s^2
Substituting the values:
Weight = 17.0 kg * 9.8 m/s^2
4. The normal force is then equal to the weight of the lawn mower:
Normal force = Weight
Finally, let's solve part (d) and calculate the force required to accelerate the lawn mower:
Using Newton's second law again, we can calculate the force needed to accelerate the lawn mower:
5. Calculate the acceleration of the lawn mower:
Acceleration = (final velocity - initial velocity) / time
Given:
initial velocity = 0 m/s (rest)
final velocity = 1.3 m/s
time = 2.0 s
Substituting the values:
Acceleration = (1.3 m/s - 0 m/s) / 2.0 s
6. Calculate the force required using Newton's second law:
Force = mass * acceleration
Given:
mass = 17.0 kg
acceleration = calculated in step 5
Substituting the values:
Force = 17.0 kg * calculated acceleration
Now, you can plug in the values into the equations and calculate the answers for parts (b), (c), and (d) of the problem.