The rocket sled shown in Figure 4.5 accelerates at a rate of 29.0 m/s2. Its passenger has a mass of 66.0 kg.
Calculate the direction and magnitude of the total force the seat exerts against his body.
Magnitude:
F=ma
Direction: see figure.
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To calculate the direction and magnitude of the total force exerted by the seat on the passenger, we can apply Newton's second law of motion, which states that the net force acting on an object is equal to the product of its mass and acceleration.
Given:
Acceleration of the rocket sled, a = 29.0 m/s^2
Mass of the passenger, m = 66.0 kg
Step 1: Calculate the force acting on the passenger using the formula:
Force = mass × acceleration
Force = 66.0 kg × 29.0 m/s^2
Force = 1914 kg⋅m/s^2 or N (Newtons)
Step 2: Determine the direction of the force.
Since the acceleration is positive and in the same direction as the rocket sled's motion, the force exerted by the seat on the passenger will also be in the same direction. Therefore, the force is directed along the motion of the rocket sled.
Therefore, the direction of the force exerted by the seat against the passenger's body is the same as the direction of the acceleration, which is in the direction of the rocket sled's motion.
Step 3: Calculate the magnitude of the force.
The magnitude of the force is the absolute value of the force calculated in step 1. In this case, it is:
Magnitude of the force = 1914 N
So, the magnitude of the total force exerted by the seat against the passenger's body is 1914 Newtons, and it is directed in the same direction as the acceleration of the rocket sled.