8kg mass moving with a speed of 30ms^-1 is brought to rest in 2.5s by a constant retarding force.calculate the magnitude of the force.
acceleration= velocitychange/time
force*time= changemomentum= mass*changevelocty
force= mass*changevelocity/time
force= 8*30/2.5 N
To calculate the magnitude of the force, we can use the formula:
Force = (mass * change in velocity) / time
Given:
Mass (m) = 8 kg
Initial velocity (u) = 30 m/s
Final velocity (v) = 0 m/s
Time (t) = 2.5 s
Change in velocity (Δv) = v - u = 0 - 30 = -30 m/s
Now we can substitute the values into the formula to calculate the magnitude of the force:
Force = (mass * change in velocity) / time
Force = (8 kg * -30 m/s) / 2.5 s
Calculating the magnitude of the force:
Force = (-240 kg·m/s) / 2.5 s
Force = -96 N
Therefore, the magnitude of the force is 96 N (note that the negative sign indicates that the force is acting in the opposite direction of the initial velocity).
To calculate 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.
In this case, the object is brought to rest from a certain speed in a certain time period, so we need to find the acceleration first.
We can use the equation of motion:
v = u + at
Where:
v = final velocity (0 m/s, as the object comes to rest)
u = initial velocity (30 m/s)
a = acceleration (to be calculated)
t = time taken (2.5 seconds)
Rearranging the equation to solve for acceleration:
a = (v - u) / t
Plugging in the values:
a = (0 - 30) / 2.5
a = -30 / 2.5
a = -12 m/s^2
Note: The negative sign indicates that the acceleration is in the opposite direction to the initial velocity, as the object is being slowed down.
Now that we have the acceleration, we can calculate the magnitude of the force using Newton's second law:
F = m * a
Plugging in the values:
F = 8 kg * (-12 m/s^2)
F = -96 N
The magnitude of the force is 96 N, with a negative sign indicating that the force is in the opposite direction to the initial velocity of the object.