A motor of mass30kg moving with a velocity of 10m/s by application of brakes is brought to rest in a distance of 25m .find the average force
To find the average force applied to bring the motor to rest, we can use the equation for average force:
Average Force = (Change in momentum) / (Time taken)
Step 1: Find the change in momentum.
Momentum (p) is given by the product of mass (m) and velocity (v):
Momentum = mass × velocity
= m × v
Initial momentum (p₁) = mass × initial velocity
= 30 kg × 10 m/s
Final momentum (p₂) = mass × final velocity
= 30 kg × 0 m/s
Change in momentum = Final momentum - Initial momentum
= p₂ - p₁
Step 2: Find the time taken.
The time taken can be calculated using the equation of motion:
Distance = Initial velocity × Time + (1/2) × Acceleration × Time²
Since the motor is brought to rest, the final velocity is 0 m/s, and the acceleration is in the opposite direction to the initial velocity (as brakes are applied):
Distance = Initial velocity × Time + (1/2) × (-acceleration) × Time²
Substituting the given values:
25 m = 10 m/s × Time + (1/2) × (-acceleration) × Time²
Solving this equation will give us the time taken.
Step 3: Calculate average force.
Now, we can use the formula for average force:
Average Force = Change in momentum / Time taken
Substitute the values we calculated for the change in momentum and time taken into this equation to find the average force.
V^2 = Vo^2 + 2a*d.
0 = 10^2 + 2a*25,
a = -2 m/s^2.
F = M*a.