a constant force acts for 3s on a body of mass 16kg and then ceases to act.during the next 3s,the body covers 81m.find the magnitude of the force.
288Nis answer
To find the magnitude of the force, we can use Newton's second law of motion, which states that the force acting on an object is equal to the product of its mass and acceleration.
First, let's find the acceleration of the body during the time the force is acting. We can use the formula:
acceleration = force / mass
Given that the mass of the body is 16 kg, we'll substitute it into the equation:
acceleration = force / 16 kg
To determine the acceleration, we need to find the distance covered by the body during the 3 seconds when the force is acting. We know that the formula to calculate distance is:
distance = initial velocity × time + 0.5 × acceleration × time^2
Given the distance covered during this time is 81 m and the time is 3 seconds, we can substitute these values into the equation and solve for acceleration:
81 m = 0 + 0.5 × acceleration × (3 s)^2
81 m = 4.5 × acceleration
acceleration = 81 m / 4.5 s^2
acceleration = 18 m/s^2
Now that we have the known acceleration, we can substitute it into the equation for acceleration:
18 m/s^2 = force / 16 kg
To solve for the force, we'll multiply both sides of the equation by 16 kg:
force = 18 m/s^2 × 16 kg
force = 288 N
Therefore, the magnitude of the force is 288 N.
To find the magnitude of the force, 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:
F = m * a
First, we need to find the acceleration of the body. We can use the equation of motion:
d = v0 * t + 0.5 * a * t^2
where:
d = distance traveled (81 m)
v0 = initial velocity (0 m/s, as the body was initially at rest)
t = time (3 s)
Since the body was initially at rest, the equation can be simplified to:
d = 0.5 * a * t^2
Rearranging the equation, we have:
a = (2 * d) / (t^2) = (2 * 81) / (3^2) = 18 m/s^2
Now we can calculate the force:
F = m * a = 16 kg * 18 m/s^2 = 288 N
Therefore, the magnitude of the force acting on the body is 288 Newtons.
assuming no friction, its final velocity is 81/3 m/s
Vf=a*t= Force/mass * t
solve for force.