A person pushes a 14.5 kg lawnmower at constant speed with a force of 88 N directed along the handle, which is at an angle of 45o to the horizontal.
What is the force required to accelerate it from rest to 1.5 m/s in 2.5 seconds?
You know the pushing force for constant velocity, so the horizontal component of the pushing force must be friction. Find that.
Now
Forcenet=forcefriction+ Mass*acceleration.
Solve for the net force, knowing mass, acceleration, and the force of friction.
71
To solve this problem, we can use Newton's second law of motion, which states that the force acting on an object is equal to the mass of the object multiplied by its acceleration. The formula for this is:
F = m * a
Where F is the force, m is the mass, and a is the acceleration.
In this case, the lawnmower has a mass of 14.5 kg and is being accelerated from rest to 1.5 m/s in 2.5 seconds. We can calculate the acceleration using the formula:
a = (v - u) / t
Where v is the final velocity, u is the initial velocity, and t is the time taken.
Given:
mass (m) = 14.5 kg
initial velocity (u) = 0 m/s
final velocity (v) = 1.5 m/s
time (t) = 2.5 s
Plugging in the values, we have:
a = (1.5 - 0) / 2.5
a = 1.5 / 2.5
a = 0.6 m/s^2
Now, we can calculate the force required using Newton's second law:
F = m * a
F = 14.5 kg * 0.6 m/s^2
F ≈ 8.7 N
Therefore, the force required to accelerate the lawnmower from rest to 1.5 m/s in 2.5 seconds is approximately 8.7 N.
To find the force required to accelerate the lawnmower from rest to 1.5 m/s in 2.5 seconds, we can use Newton's second law of motion, which states that force (F) is equal to mass (m) multiplied by acceleration (a): F = m * a.
Given:
Mass of the lawnmower (m) = 14.5 kg
Initial velocity (u) = 0 m/s (since it's at rest)
Final velocity (v) = 1.5 m/s
Time taken (t) = 2.5 seconds
First, we can calculate the acceleration (a) using the formula:
a = (v - u) / t
Substituting the given values:
a = (1.5 m/s - 0 m/s) / 2.5 s
a = 0.6 m/s²
Now, we can use Newton's second law to find the force (F):
F = m * a
F = 14.5 kg * 0.6 m/s²
F = 8.7 N
Therefore, the force required to accelerate the lawnmower from rest to 1.5 m/s in 2.5 seconds is 8.7 Newtons.