Sample problem on inertia
Problem:
A 2 kg block is moving with a velocity of 4 m/s towards the right. A force of 10 N is applied on the block in the opposite direction. Calculate the acceleration of the block and the time it will take to stop.
Solution:
Given:
Mass of the block (m) = 2 kg
Initial velocity (u) = 4 m/s
Force (F) = 10 N
Using Newton's second law of motion, we can calculate the acceleration:
F = ma
Where,
F = Force applied
m = Mass of the block
a = Acceleration
Rearranging the equation:
a = F/m
Substituting the given values:
a = 10 N / 2 kg
= 5 m/s²
Therefore, the acceleration of the block is 5 m/s².
To calculate the time it will take for the block to stop, we can use the equation:
v = u + at
Where,
v = Final velocity (zero in this case, since the block comes to rest)
u = Initial velocity
a = Acceleration
t = Time
Rearranging the equation:
t = (v - u) / a
Substituting the given values:
t = (0 - 4 m/s) / -5 m/s²
= 4/5 s
= 0.8 s
Therefore, it will take 0.8 seconds for the block to stop.
Problem: A 5 kg box is initially at rest. A force of 20 N is applied to the box for 2 seconds in the positive direction. Find the final velocity of the box.
Solution:
Step 1: Determine the initial velocity of the box.
Since the box is initially at rest, the initial velocity (u) is 0 m/s.
Step 2: Calculate the acceleration experienced by the box.
Using Newton's second law of motion, we can find the acceleration (a) experienced by the box:
F = m * a
20 N = 5 kg * a
a = 20 N / 5 kg
a = 4 m/s^2
Step 3: Determine the final velocity of the box.
We can use the equation of motion to calculate the final velocity (v) of the box:
v = u + a * t
v = 0 m/s + (4 m/s^2) * 2 s
v = 0 m/s + 8 m/s
v = 8 m/s
Therefore, the final velocity of the box is 8 m/s.
Sure! Here's a sample problem on inertia:
Problem: A bowling ball with a mass of 5 kilograms is initially at rest. When a force of 10 Newtons is applied to the ball for a duration of 2 seconds, what will be its final velocity?
To solve this problem, we'll need to 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, we can rearrange the formula to solve for acceleration:
Force = mass * acceleration
Acceleration = Force / mass
Now, we can use the formula for average velocity to find the final velocity:
Average velocity = initial velocity + (acceleration * time)
Since the bowling ball is initially at rest, its initial velocity is 0. Plugging in the values into the formula:
Average velocity = 0 + (acceleration * time)
We already know the time is 2 seconds, so we'll substitute it in the equation:
Average velocity = 0 + (acceleration * 2)
Now, let's find the acceleration using Newton's second law of motion:
Acceleration = Force / mass
Acceleration = 10 N / 5 kg
Acceleration = 2 m/s^2
Substituting this value into the equation for average velocity:
Average velocity = 0 + (2 m/s^2 * 2 s)
Average velocity = 4 m/s
Therefore, the final velocity of the bowling ball will be 4 meters per second.