The handle of a 27kg lawnmower makes a 36∘ angle with the horizontal.
If the coefficient of friction between lawnmower and ground is 0.66, what magnitude of force, applied in the direction of the handle, is required to push the mower at constant velocity?
Express your answer using two significant figures.
Compare with the mower’s weight.
Express your answer using two significant figures.
Well, well, well! Looks like we have a situation that requires some calculations. Let's get to it!
To find the force required to push the lawnmower at constant velocity, we need to consider the forces acting on it. We have the gravitational force pulling it downwards, and the force of friction opposing its motion.
The gravitational force can be calculated by multiplying the mass of the lawnmower (27kg) by the acceleration due to gravity (9.8 m/s^2). So, the weight of the lawnmower is approximately 264 N.
Now, to determine the force of friction, we can use the equation: Frictional force = coefficient of friction * normal force. The normal force is simply the component of the weight perpendicular to the ground, which is equal to the weight multiplied by the cosine of the angle (36∘). Hence, the normal force is approximately 211 N (calculated as 264 N * cos(36∘)).
Plugging the values into the equation, the frictional force is approximately 139 N (0.66 * 211 N).
To keep the mower moving at constant velocity, we need to apply a force equal in magnitude and opposite in direction to the frictional force. So the force required to push the mower at constant velocity is approximately -139 N.
If we compare this force to the weight of the lawnmower, we can see that it's less. The force required to push the mower is approximately 139 N, while the weight of the lawnmower is approximately 264 N. So the force required is less than the weight.
I hope that helps, and remember, clowning around with calculations can make them less boring!
To find the magnitude of force required to push the lawnmower at constant velocity, we need to consider the forces acting on the lawnmower.
1. Weight of the lawnmower (force due to gravity):
The weight is given as 27 kg. The weight force is equal to the mass multiplied by the acceleration due to gravity (9.8 m/s^2).
Weight = mass * acceleration due to gravity
Weight = 27 kg * 9.8 m/s^2 = 264.6 N
2. Normal force:
The normal force is the force exerted by the ground on the lawnmower, perpendicular to the surface. In this case, it is equal to the weight of the lawnmower (since the lawnmower is on a flat surface).
3. Frictional force:
The frictional force opposes the motion of the lawnmower and acts parallel to the surface. The force of static friction can be calculated using the coefficient of friction (0.66) and the normal force.
Frictional force = coefficient of friction * normal force
Since the lawnmower is at constant velocity, the applied force must be equal to the frictional force.
4. Applied force:
Let's assume the applied force is F.
Now, using trigonometry, we can find the horizontal component of the applied force:
Horizontal component of the applied force = Applied force * cos(angle)
Horizontal component of the applied force = F * cos(36∘)
Since the magnitude of the force required to push the lawnmower at constant velocity is equal to the frictional force, we have:
F * cos(36∘) = coefficient of friction * normal force
Substituting the values we have:
F * cos(36∘) = 0.66 * 264.6 N
F * cos(36∘) ≈ 174.84 N
To compare with the mower's weight, we can divide the magnitude of the force required by the weight of the lawnmower:
Force required / Weight of the lawnmower = 174.84 N / 264.6 N ≈ 0.66
Therefore, the magnitude of force required to push the mower at constant velocity is approximately 174.84 N, which is about 0.66 times the weight of the lawnmower.
To solve this problem, we can use the concept of friction and forces. The force required to push the lawnmower at constant velocity can be found by considering the horizontal forces acting on it.
First, let's calculate the weight of the lawnmower. The weight of an object is given by the formula:
Weight = mass × acceleration due to gravity
Given that the mass is 27 kg and the acceleration due to gravity is approximately 9.8 m/s², we can calculate the weight of the lawnmower:
Weight = 27 kg × 9.8 m/s² = 264.6 N (rounded to 2 significant figures)
Now, let's consider the forces acting on the lawnmower. The main forces are the weight acting downward and the frictional force opposing the motion. Since the lawnmower is moving at constant velocity, the force we need to find is equal to the frictional force.
The frictional force can be calculated using the equation:
Frictional force = coefficient of friction × normal force
The normal force is equal to the perpendicular component of the weight, which is given by:
Normal force = weight × cosine(angle)
Given that the angle is 36∘, we can calculate the normal force:
Normal force = 264.6 N × cos(36∘) ≈ 217.63 N (rounded to 2 significant figures)
Now we can calculate the frictional force:
Frictional force = 0.66 × 217.63 N ≈ 143.41 N (rounded to 2 significant figures)
So, the magnitude of the force required to push the lawnmower at constant velocity is approximately 143.41 N (rounded to 2 significant figures).
To compare this with the mower's weight, we simply calculate the ratio of the two:
Ratio = (Force required to push the lawnmower) / (Weight of the lawnmower)
Ratio = 143.41 N / 264.6 N ≈ 0.5427 (rounded to 2 significant figures)
Therefore, the magnitude of the force required to push the lawnmower at constant velocity is approximately 0.5427 times the weight of the lawnmower (rounded to 2 significant figures).
M*g = 27 * 9.8 = 264.6 N. = Wt. of the lawnmower.
Fn = 264.6 + Fap*sin36=264.6 + 0.588Fap
Fk = u*Fn = 0.66*(264.6+0.588Fap) =
174.64 + 0.388Fap
(Fx-Fk) = M*a
(Fap*Cos36-(174.64+0.388Fap) = M*a
(0.81Fap-174.64-0.388Fap = M*0
0.42Fap - 174.64 = 0
0.42Fap = 174.64
Fap = 416 N. = Force applied.