there's three parts, i keep getting these wrong please help.
A set of crash tests consists of running a test car moving at a speed of 11.8 m/s (26.4 mi/hr) into a solid wall. Strapped securely in an advanced seat belt system, a 59.0 kg (130 lbs) dummy is found to move a distance of 0.660 m from the moment the car touches the wall to the time the car is stopped. Calculate the size of the average force which acts on the dummy during that time.
Using the direction of motion as the positive direction, calculate the average acceleration of the dummy during that time (in g's, with 1g = 9.81m/s2).
In a different car, the distance the dummy moves while being stopped is reduced from 0.660 m to 0.210 m,
calculate the average force on the dummy as that car stops.
(Average belt force)x (distnce moved)
= initial kinetic energy of dummy
= (1/2)*59 kg* (11.8 m/s)^2 = 4108 J
Avg. Force = 4108/.66 = 6224 Newtons
Acceleration is backwards (negative sign) and equals the speed change divided by time intervsl
sqrt (-2aX) = V
a = -V^2/(2X) = -105.5 m/s^2
= -10.75 g's
Repeat the same method for the second case. The force must be larger to stop in a reduced distance
To calculate the average force acting on the dummy during the collision, you can use Newton's second law of motion, which states that force (F) is equal to mass (m) multiplied by acceleration (a), represented by the equation F = ma.
First, let's find the average force acting on the dummy in the first scenario:
Given:
Initial velocity of the car (v) = 11.8 m/s
Distance moved by the dummy (d) = 0.660 m
Mass of the dummy (m) = 59.0 kg
Step 1: Find the time taken to stop the car.
Using the equation v = at, where v = 0 (since the car stops), and t is the time taken to stop.
0 = at
t = 0 since acceleration is instantaneous.
Step 2: Calculate the acceleration.
Using the equation d = (1/2)at², where d = distance, a = acceleration, and t = time taken.
0.660 m = (1/2)(a)(0)² [since t = 0]
0 = 0.330a
a = 0 m/s².
Step 3: Calculate the average force using F = ma.
F = (59.0 kg)(0 m/s²)
F = 0 N (Newtons).
Therefore, in the first scenario, the size of the average force acting on the dummy during the collision is 0 Newtons. This implies that the dummy does not experience any force.
Now, let's calculate the average force acting on the dummy in the second scenario:
Given:
Initial velocity of the car (v) = 11.8 m/s
Distance moved by the dummy (d) = 0.210 m
Mass of the dummy (m) = 59.0 kg
Step 1: Find the time taken to stop the car.
Using the equation v = at.
0 = at
t = 0 since acceleration is instantaneous.
Step 2: Calculate the acceleration.
Using the equation d = (1/2)at².
0.210 m = (1/2)(a)(0)² [since t = 0]
0 = 0.105a
a = 0 m/s².
Step 3: Calculate the average force using F = ma.
F = (59.0 kg)(0 m/s²)
F = 0 N (Newtons).
Therefore, in the second scenario, the size of the average force acting on the dummy during the collision is 0 Newtons. Again, this implies that the dummy does not experience any force.
In both scenarios, since the dummy does not undergo any deceleration, the average force acting on the dummy is 0 Newtons.