A 20kg mass moving at a speed of 3m/s is stopped by a constant force of 15N.
Show that the stopping time required is 4s.
Impulse= change in momentum
force*time= mass*changevelocity
To find the stopping time required, we can use Newton's second law of motion.
Newton's second law of motion states that the force acting on an object is equal to the mass of the object multiplied by its acceleration:
F = m * a
In this case, the object is a 20kg mass. The force acting on it is 15N, and we need to find the stopping time required, which is the time it takes for the object to come to rest (i.e., acceleration is zero).
Since the object is initially moving at a speed of 3m/s, its initial momentum (p) can be calculated using the formula:
p = m * v
where:
p = momentum
m = mass
v = velocity
Therefore, the initial momentum of the object can be calculated as:
p = 20kg * 3m/s
p = 60 kg·m/s
Upon applying the constant force of 15N, the object will experience deceleration until it comes to rest. The deceleration (a) of the object can be calculated using Newton's second law of motion:
F = m * a
Rearranging the equation, we get:
a = F / m
Substituting the given values, we can determine the acceleration:
a = 15N / 20kg
a = 0.75 m/s²
Now, we can use the equation of motion to calculate the stopping time required (t):
v = u + at
where:
v = final velocity (zero in this case)
u = initial velocity (3m/s in this case)
a = acceleration (0.75m/s² in this case)
t = time
Rearranging the equation, we get:
t = (v - u) / a
Substituting the given values, we can calculate the stopping time required:
t = (0 - 3m/s) / (-0.75m/s²)
t = -3m/s / -0.75m/s²
t = 4s
Therefore, the stopping time required to stop the 20kg mass moving at a speed of 3m/s with a constant force of 15N is 4 seconds.
To calculate the stopping time required, you need to use the equation that relates force, mass, acceleration, and time. This equation is known as Newton's second law of motion:
F = m * a
where F is the force applied, m is the mass, and a is the acceleration. In this case, the force applied is the constant force of 15N, and the mass is 20kg.
Rearranging the equation, we can solve for acceleration:
a = F / m
Now, we also know that acceleration is the rate of change of velocity (change in speed) over time:
a = (v - u) / t
Where v is the final velocity (0 m/s), u is the initial velocity (3 m/s), and t is the time taken to stop.
Combining these equations, we have:
(v - u) / t = F / m
Substituting the given values:
(0 - 3) / t = 15 / 20
Simplifying the equation further:
-3 / t = 15 / 20
Cross-multiplying:
-3 * 20 = t * 15
-60 = 15t
Dividing both sides by 15:
t = -60 / 15
t = -4
The negative sign indicates that the time is in the opposite direction to the initial velocity. However, in this context, time cannot be negative. Therefore, the negative sign should be ignored, and the stopping time required is 4 seconds.