A car traveling at 20 m/s stops in a distance of 50 m.
Assume that the deceleration is constant. The coefficients of
friction between a passenger and the seat are µs = 0.5 and
µk = 0.03. Will a 70-kg passenger slide off the seat if not
wearing a seat belt?
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F=ma
V=u+2as
yes
To determine if the passenger will slide off the seat, we need to consider the maximum force of static friction between the passenger and the seat. If this force is greater than or equal to the force experienced by the passenger due to deceleration, then the passenger will not slide off the seat.
To calculate the maximum force of static friction (Fsf), we can use the formula:
Fsf = µs * N
where µs is the coefficient of static friction and N is the normal force.
The normal force (N) acting on the passenger is equal to the passenger's weight, which can be calculated using the formula:
N = m * g
where m is the mass of the passenger (70 kg) and g is the acceleration due to gravity (approximately 9.8 m/s²).
Substituting the values, we get:
N = 70 kg * 9.8 m/s² = 686 N
Now we can calculate the maximum force of static friction:
Fsf = 0.5 * 686 N = 343 N
Next, we need to calculate the force experienced by the passenger due to deceleration.
The force (F) experienced by the passenger is equal to the mass of the passenger (70 kg) multiplied by the deceleration (a) of the car.
Using the formula:
F = m * a
We can rearrange the formula to solve for the deceleration:
a = F / m
Assuming the deceleration is constant, we can calculate it using the formula:
a = (v_f - v_i) / t
where v_f is the final velocity (0 m/s), v_i is the initial velocity (20 m/s), and t is the time taken to stop.
Since we know the initial velocity and distance traveled, we can use the formula:
t = d / v_i
Substituting the values, we get:
t = 50 m / 20 m/s = 2.5 s
Now we can calculate the deceleration:
a = (0 m/s - 20 m/s) / 2.5 s = -8 m/s²
Note that the deceleration is negative because it opposes the motion.
Finally, we can calculate the force experienced by the passenger:
F = 70 kg * (-8 m/s²) = -560 N
Since the force experienced by the passenger due to deceleration (-560 N) is less than the maximum force of static friction (343 N), the passenger will not slide off the seat if not wearing a seat belt. The force of static friction between the passenger and the seat is greater than the force experienced due to deceleration.