A racing car starting from a standstill can reach a speed of 320 km/h in 6.50 s by exerting an average horizontal force of 1.52 x 10^4N [s] on the pavement. If friction equals 5.2 x 10^3 N, what is the mass of the car?
a = 320km/hr / 6.5s * 1000m/1km * 1hr/3600s = 13.68 m/s^2
Since F = ma, the net force is 13.68m
Since the net force is 1.52*10^4-5.2*10^3, divide that by a to get m.
Well, to solve this problem, we need to use Newton's second law of motion. But let's not get too serious, we can still have some fun with physics! So, we have a racing car that's trying to zoom from 0 to 320 km/h in 6.50 seconds. Talk about a need for speed!
Now, we know that the average force exerted on the pavement is 1.52 x 10^4 N [s], and the friction between the car and the pavement is 5.2 x 10^3 N. So, the net force acting on the car is the difference between these two forces. It's like the battle of pushing and pulling.
To find the mass of the car, we can use the equation F = ma, where F is the net force, m is the mass, and a is the acceleration. In this case, the acceleration is the change in velocity divided by the time it takes to change that velocity. Phew, that's a lot to take in!
To convert the velocity from km/h to m/s, we need to divide it by 3.6. So, 320 km/h becomes 88.9 m/s. Now, dividing this velocity by the time of 6.50 seconds, we get an acceleration of approximately 13.7 m/s^2.
Now, let's put everything together. The net force is the average force minus the friction force, which gives us a value of 1.52 x 10^4 N [s] - 5.2 x 10^3 N = 1.0 x 10^4 N.
Now, using Newton's second law, we can rearrange the equation to solve for mass: m = F / a. Plugging in the values, we get the mass of the car to be approximately 7.30 x 10^2 kg.
So, my friend, the mass of the car is 7.30 x 10^2 kg. That's quite a hefty racer! I hope this answer zoomed right into your heart! Keep racing and keep smiling!
To find the mass of the car, we can use Newton's second law of motion:
F = ma
Given:
Average horizontal force exerted by the car on the pavement (F) = 1.52 x 10^4 N
Friction (f) = 5.2 x 10^3 N
According to Newton's second law, the net force acting on the car is the difference between the force exerted by the car and the friction:
Net Force (F_net) = F - f
Now, the net force can also be expressed as:
F_net = ma
We can rearrange the equation to solve for mass (m):
m = F_net / a
We need to calculate the acceleration (a) of the car. The formula for acceleration is:
a = Δv / Δt
Given:
Initial velocity (u) = 0 (car starts from a standstill)
Final velocity (v) = 320 km/h = (320 * 1000) m/3600 s = 88.89 m/s
Time taken (Δt) = 6.50 s
Substituting these values into the formula for acceleration, we get:
a = (v - u) / t
a = (88.89 - 0) / 6.50
a = 13.68 m/s^2
Now, substituting the values of net force (F_net) and acceleration (a) into the equation for mass:
m = F_net / a
m = (1.52 x 10^4) / 13.68
m ≈ 1111 kg
Therefore, the mass of the car is approximately 1111 kg.
To find the mass of the car, we can make use of Newton's Second Law of Motion, which states that the force exerted on an object is equal to the mass of the object multiplied by its acceleration:
F = m * a
In this case, the force exerted on the car is the difference between the average horizontal force exerted by the car and the friction force:
F_net = F_applied - F_friction
Given that the net force is equal to the mass of the car multiplied by its acceleration, we can rewrite the equation as:
m * a = F_applied - F_friction
We are given the force exerted by the car (F_applied = 1.52 x 10^4 N) and the friction force (F_friction = 5.2 x 10^3 N) in the problem statement. We need to find the acceleration (a) to solve for the mass (m) of the car.
The acceleration can be calculated using the formula for average acceleration:
a = (vf - vi) / t
Where vf is the final velocity, vi is the initial velocity (which is 0 in this case since the car starts from a standstill), and t is the time taken (which is given as 6.50 s).
Substituting the given values, we get:
a = (320 km/h - 0 km/h) / 6.50 s
Before we solve for the acceleration, we need to convert the velocity from km/h to m/s, since the SI unit for acceleration is m/s^2.
1 km/h = 1000 m/3600 s ≈ 0.278 m/s
Substituting this conversion into the equation:
a = (320 km/h - 0 km/h) ⋅ (1000 m/3600 s) / 6.50 s
Now we can calculate the acceleration:
a = (320 ⋅ 0.278) / 6.50 m/s²
Next, we substitute the values into the equation m * a = F_applied - F_friction :
m * [(320 ⋅ 0.278) / 6.50] = 1.52 x 10^4 N - 5.2 x 10^3 N
Finally, we rearrange the equation to solve for the mass (m):
m = (1.52 x 10^4 N - 5.2 x 10^3 N) / [(320 ⋅ 0.278) / 6.50]
Evaluating this expression will give us the mass of the car.