A car of mass 1000kg moving with a velocity of 36km/h hits a wall and comes to rest in 5s.find the force and work done by the car on the wall.
36 km/h = 36000m/3600 s = 10 m/s
Car's initial momentum = 10^3*10
= 10^4 kg*m/s
Divide that by the stopping time (5 s) to get the average force, in newtons.
The "work done by the car" is the initial kinetic energy of the car,
(1/2)MVo^2 = 5*10^4 J,
but it is mostly converted to heat and inelastic damage distortion of the wall and the car itself.
please answer correctly
To find the force and work done by the car on the wall, we can use the principles of Newton's laws of motion and energy.
Step 1: Convert the velocity from km/h to m/s.
Given: Velocity (v) = 36 km/h
Convert km/h to m/s by multiplying by 1000/3600.
v = 36 km/h * (1000 m/ 1 km) * (1h / 3600 s)
v = 10 m/s
Step 2: Calculate the acceleration using the equation:
Acceleration (a) = (final velocity - initial velocity) / time
Given: initial velocity (u) = 10 m/s
final velocity (v) = 0 m/s
time (t) = 5 s
a = (0 m/s - 10 m/s) / 5 s
a = -2 m/s²
Step 3: Calculate the force using Newton's second law of motion:
Force (F) = mass (m) * acceleration (a)
Given: mass (m) = 1000 kg
F = 1000 kg * -2 m/s²
F = -2000 N (Note: The negative sign indicates that the force is acting in the opposite direction of the car's motion.)
Step 4: Calculate the work done by the car on the wall using the work-energy principle:
Work (W) = force (F) * displacement (s)
Given: force (F) = -2000 N
displacement (s) = ? (We need more information to calculate the displacement)
Without the value of displacement (s), we cannot calculate the work done by the car on the wall.
To find the force and work done by the car on the wall, we can use the equations of motion.
First, let's convert the velocity from km/h to m/s. We know that 1 km/h is equal to 1000 m/3600 s.
So, velocity = 36 km/h = (36 x 1000) m/3600 s = 10 m/s.
Given:
Mass of the car, m = 1000 kg
Initial velocity, u = 10 m/s
Final velocity, v = 0 m/s (as the car comes to rest)
Time, t = 5 s
The first equation of motion is:
v = u + at
Since the car comes to rest, v = 0, and therefore, the equation becomes:
0 = 10 + a x 5
Simplifying, we can find the acceleration (a) of the car:
a = -10/5 = -2 m/s²
The negative sign indicates that the car decelerated or accelerated in the opposite direction to its initial motion.
Next, we can find the force acting on the car:
The second equation of motion is:
v² = u² + 2as
Plugging in the known values:
0 = 10² + 2 x (-2) x s
Simplifying, we find that the distance traveled by the car (s) before coming to rest is:
s = -100/4 = -25 m (using the positive value)
Now, to find the force (F) applied by the car on the wall, we can use Newton's second law of motion:
F = ma
Plugging in the values:
F = 1000 kg x -2 m/s² = -2000 N (using the positive value)
The negative sign indicates that the force is acting in the opposite direction to the car's initial motion. It means the wall exerts a force on the car, causing it to come to rest.
Finally, to find the work done by the car on the wall, we can use the work-energy principle. The work done (W) is given by:
W = 0.5mv² - 0.5mu²
Plugging in the known values:
W = 0.5 x 1000 kg x 0² - 0.5 x 1000 kg x 10²
Simplifying, the work done by the car on the wall is:
W = -50000 J (using the negative value)
Again, the negative sign indicates that the work done is in the opposite direction to the car's initial motion, meaning work is done by the wall on the car.
Therefore, the force applied by the car on the wall is -2000 N, and the work done by the car on the wall is -50000 J.