A 2200-kg sport utility vehicle traveling at 96 km/h can be stopped in 0.21 s if it hits a concrete wall. Assume a 60 kg person was in the car that hit this wall. The velocity of the person equals that of the car both before and after the crash, and the velocity changes in 0.21 s.
(a)(a) What is the average force exerted on the person? N
(B)Some people think that they can stop themselves rushing forward by putting their hands on the dashboard. Find the mass of the object that has a weight equal to the force you just calculated.
kg
To find the average force exerted on the person, we can use Newton's second law of motion, which states that force (F) is equal to the mass (m) of an object multiplied by its acceleration (a):
F = m * a
In this case, the acceleration can be calculated using the formulas for average acceleration:
a = (change in velocity) / (time taken)
First, let's convert the velocity from km/h to m/s:
96 km/h = 96 * (1000 m / 3600 s) = 26.67 m/s
Since the velocity of the person is the same as the car before and after the crash, the change in velocity is 0. Therefore, the acceleration is:
a = (0 m/s - 26.67 m/s) / 0.21 s = -126.86 m/s²
The negative sign indicates deceleration (opposite direction of motion).
Now, we can calculate the force using the mass of the person:
m = 60 kg
F = 60 kg * (-126.86 m/s²) ≈ -7611.6 N
Therefore, the average force exerted on the person is approximately 7611.6 N.
To find the mass of an object that has a weight equal to the force calculated, we can use the equation for weight:
weight = mass * acceleration due to gravity (g)
Since the force calculated is equal to the weight, we can equate the two:
-mass * 9.8 m/s² = -7611.6 N
Dividing both sides by -9.8 m/s², we get:
mass = 7611.6 N / 9.8 m/s² ≈ 777.4 kg
Therefore, the mass of an object that has a weight equal to the force calculated is approximately 777.4 kg.
To solve this problem, we need to use the principle of conservation of momentum.
(a) To find the average force exerted on the person, we can calculate the change in momentum of the car and person during the collision.
The initial momentum of the car and person is given by:
Initial momentum = mass * velocity
Given:
Mass of the car = 2200 kg
Velocity of the car before the crash = 96 km/h (convert to m/s: 96 km/h * 1000 m/km * 1/3600 h/s = 26.67 m/s)
Mass of the person = 60 kg
The final momentum of the car and person is zero since they come to a stop after the collision.
Using the principle of conservation of momentum, we have:
Initial momentum = Final momentum
(2200 kg * 26.67 m/s) + (60 kg * 26.67 m/s) = 0
Simplifying this equation, we get:
59274 kg*m/s + 1600.2 kg*m/s = 0
To find the average force exerted on the person, we use the formula:
Average force = Change in momentum / Change in time
Change in momentum = Final momentum - Initial momentum = 0 - (2200 kg * 26.67 m/s)
Given that the change in time is 0.21 s, we can now calculate the average force:
Average force = (2200 kg * -26.67 m/s) / 0.21 s
= -59274 N
Therefore, the average force exerted on the person is -59274 N. The negative sign indicates that the force acts in the opposite direction of the initial motion.
(b) To find the mass of the object with a weight equal to the force exerted on the person, we can use Newton's second law, which states that the weight of an object is equal to the force acting on it.
Weight = mass * acceleration due to gravity
Given that the force exerted on the person is -59274 N, we can equate it to the weight of the object:
-59274 N = mass * 9.8 m/s^2
Solving for mass:
mass = -59274 N / 9.8 m/s^2
However, a negative mass doesn't have any physical meaning, so we can disregard the negative sign and take the magnitude:
mass ≈ 6045 kg
Therefore, the mass of the object that has a weight equal to the force exerted on the person is approximately 6045 kg.
change in v = 96*10^3/3.6*10^3 = 26.7 m/s
acceleration = change in v/time
26.7/.21 = 127 m/s^2
F = m a = 60*127 = 7619 Newtons
m g = 7619
m = 777 kilograms
(about 1700 pounds weight)