Driving in your car with a constant speed of v= 22 m/s, you encounter a bump in the road that has a circular cross-section, as indicated in the figure.
If the radius of curvature of the bump is 52 m, find the apparent weight of a 66-kg person in your car as you pass over the top of the bump. pls help if i did it right
w=66(9.8_22^2/52)= 32.44is this right
To determine the apparent weight of a person in the car as it passes over the top of the bump, you need to consider the centripetal force acting on the person.
First, let's calculate the centripetal acceleration of the car. We can use the formula for centripetal acceleration:
a = v^2 / r
where
a is the centripetal acceleration,
v is the speed of the car, and
r is the radius of curvature of the bump.
Substituting the given values, we get:
a = (22 m/s)^2 / 52 m
a ≈ 9.35 m/s^2
Now let's calculate the net force acting on the person at the top of the bump. The net force is the sum of the person's apparent weight (mg) and the centripetal force (ma):
F_net = mg + ma
Substituting the given values for the person's mass (m = 66 kg) and the calculated centripetal acceleration (a ≈ 9.35 m/s^2), we get:
F_net = 66 kg * 9.8 m/s^2 + 66 kg * 9.35 m/s^2
F_net ≈ 646.8 N + 616.1 N
F_net ≈ 1262.9 N
So, the apparent weight of the person in the car as it passes over the top of the bump is approximately 1262.9 N.
To find the apparent weight of a person in the car as it passes over the top of the bump, you need to consider the forces acting on the person at that point.
When the car passes over the top of the bump, the person will experience two primary forces: their actual weight (mg) and the normal force (N) exerted by the bump. The normal force is the force exerted by a surface to support the weight of an object resting on it.
To solve this problem, we need to determine the net force acting on the person at the top of the bump.
First, calculate the actual weight of the person:
Weight = mass × gravity = 66 kg × 9.8 m/s^2 = 646.8 N
Next, let's consider the forces acting at the top of the bump. The normal force (N) will be equal to the sum of the person's weight and the centripetal force due to the car's circular motion.
Since the bump has a circular cross-section, the centripetal force acting on the person can be calculated using:
Centripetal force = mass × velocity^2 / radius of curvature
Plugging in the values:
Centripetal force = 66 kg × (22 m/s)^2 / 52 m
Now, calculate the normal force:
N = Weight + Centripetal force
Putting it all together:
N = 646.8 N + (66 kg × (22 m/s)^2 / 52 m)
Simplify and calculate the result to find the apparent weight of the person at the top of the bump.
Now let's evaluate the expression:
N = 646.8 N + (66 kg × (22 m/s)^2 / 52 m)
= 646.8 N + (66 kg × 484 m^2/s^2 / 52 m)
= 646.8 N + 646.8 N
= 1293.6 N
Therefore, the apparent weight of the 66-kg person in your car at the top of the bump is 1293.6 N, not 32.44 N.